Full Answer
How to write equation of a circle?
Writing the Equation of a Circle
- Identify the center point and the radius from the graph.
- Substitute that information back into the pattern
- Simplify.
What is the standard form equation for a circle?
- If g 2 + f 2 > c, then the radius of the circle is real.
- If g 2 + f 2 = c, then the radius of the circle is zero which tells us that the circle is a point which coincides with the centre. ...
- g 2 + f 2 <c, then the radius of the circle become imaginary. Therefore, it is a circle having a real centre and imaginary radius.
What is the parametric equation for a circle?
Parametric Equation of a Circle. A circle can be defined as the locus of all points that satisfy the equations. x = r cos(t) y = r sin(t) where x,y are the coordinates of any point on the circle, r is the radius of thecircle and. tis the parameter - the angle subtendedby the point at the circle's center.
What is the equation of a circle?
The equation of a circle is x^2 + y^2 = r^2 , where r represents the radius (with a centre at 0,0 ). The definition of a circle is a set of all points on a plane that are a fixed distance from a centre.
What is the area of a circle?
Area of the circle describes the amount of space covered by the circle and the length of the boundary of the circle is known as its circumference. r denotes the radius of the circle.
What is the length between a point on a circle and its center?
The length between any point on the circle and its center is known as its radius.Any line that passes through the center of the circle and connects two points of the circle is known as the diameter of the circle. Radius is half the length of a diameter of the circle.
What is the radius of a circle?
The radius of a circle is the distance from the centre of a circle to any point on the circle.
What is the C of a circle?
C is the circumference of the circle.
Is the diameter of a circle twice as long as the radius?
Thus, the diameter of a circle is twice as long as the radius. The area of a circle is the number of square units inside that circle. A circle has the maximum possible area for a given perimeter and the minimum possible perimeter for a given area. The perimeter C of a circle is called the circumference.
What is the Equation of a Circle?
The equation of circle with (h,k) center and r radius is given by:
What is the mathematical way to describe a circle?
The mathematical way to describe the circle is an equation. Here, the equation of the circle is provided in all the forms such as general form, standard form along with the examples.
How to find the radius of a circle?
Equation of a Circle in General Form 1 If g2 + f2 > c, then the radius of the circle is real. 2 If g2 + f2 = c, then the radius of the circle is zero which tells us that the circle is a point which coincides with the centre. Such type of circle is called a point circle 3 g2 + f2 <c, then the radius of the circle become imaginary. Therefore, it is a circle having a real centre and imaginary radius.
What is the distance between the centre and any point on the circumference called?
The fixed point is called the centre of the circle. The distance between the centre and any point on the circumference is called the radius of the circle.
How many pi is the circumference of a circle?
The circumference of a circle is equal to 2 (pi) of radius or pi of diameter.
How many units are in a radius of a circle?
Therefore, the radius of the circle is 9 units.
Is the center of a circle an origin?
Here, the centre of the circle is not an origin.
How to find circumference of a circle?
The circumference formula of a circle is obtained by multiplying the diameter by pi (π). To recall, the circumference of a closed curve or circular object is the distance around its edge. The circumference of a circle has special importance in geometry and trigonometry.
What is the C of a circle?
C is the circumference of the circle.
What is a Circle?
A circle closed plane geometric shape. In technical terms, a circle is a locus of a point moving around a fixed point at a fixed distance away from the point. Basically, a circle is a closed curve with its outer line equidistant from the center. The fixed distance from the point is the radius of the circle.
What is Area of Circle?
Area of a circle is the region covered or enclosed within its boundary. It is measured in square units.
Derivation of Area of Circle
The circle is divided into 16 equal sectors, and the sectors are arranged as shown in fig. 3. The area of the circle will be equal to that of the parallelogram-shaped figure formed by the sectors cut out from the circle. Since the sectors have equal area, each sector will have an equal arc length.
Surface Area of Circle
A circle is nothing but the 2-D representation of a sphere. The total area that is taken inside the boundary of the circle is the surface area of the circle. When we say we want the area of the circle, then we mean the surface area of the circle itself. Sometimes, the volume of a circle also defines the area of a circle.
How to Find Area of a Circle?
As we know, the area of circle is equal to pi times square of its radius, i.e. π x r 2. To find the area of circle we have to know the radius or diameter of the circle. For example, if the radius of circle is 7cm, then its area will be: Area of circle with 7 cm radius = πr 2 = π (7) 2 = 22/7 x 7 x 7 = 22 x 7 = 154 sq.cm.
Difference Between Square Area and Circle Area
The area of a circle is estimated to be 80% of area of square, when the diameter of the circle and length of side of the square is the same.
Solved Examples on Area of a Circle
We have discussed till now the different parameters of the circle such as area, perimeter or circumference, radius and diameter. Let us solve some problems based on these formulas to understand the concept of area and perimeter in a better way.
What is the formula for circumference and diameter?
Where C indicates circumference and d indicates diameter. A different way to put up this formula is C = π × d. This formula is mostly used when the diameter is mentioned, and the perimeter of a circle needs to be calculated.
What is a circle defined as?
A circle is defined as a shape with all the points are equidistant from a point at the centre. The circle depicted below has its centre lies at point A.
What is the Circumference of Circle?
The meaning of circumference is the distance around a circle or any curved geometrical shape. It is the one-dimensional linear measurement of the boundary across any two-dimensional circular surface. It follows the same principle behind finding the perimeter of any polygon, which is why calculating the circumference of a circle is also known as the perimeter of a circle.
What is the diameter of a circle in terms of circumference?
So, the diameter of the circle in terms of circumference will be equal to the ratio of the circumference of the circle and pi.
What is the proportion between the circumference of a circle and its diameter?
We know that the diameter of a circle is twice the radius. The proportion between the circumference of a circle and its diameter is equal to the value of Pi (π). Hence, we say that this proportion is the definition of the constant π.
How is a semi circle formed?
The semi-circle is formed when we divide the circle into two equal parts. Therefore, the perimeter of the semi-circle also becomes half.
What is the ratio of circumference to diameter of a circle?
Pi (π) is a special mathematical constant; it is the ratio of circumference to diameter of any circle.
How many in is the radius of a circle?
Answer: Radius of circle = 17.5 in.
What is the perimeter of a circle?
The perimeter of a circle is its boundary or the complete arc length of the periphery of a circle. The term that denotes the perimeter of a circle is called its circumference. Hence the perimeter of a circle tells us about the circumference of a circle, therefore it is also known as the circumference of a circle formula.
How To Find Circumference With Diameter Formula?
If a diameter of a circle is given then by substituting the given values in the following diameter formula we can easily find the circumference of a circle.
What is the diameter of a circle?
Diameter is one of the important parts of a circle. The straight line connecting a point from one end of the circle to a point on the other end of the circle and passing through the center is called a diameter. Since there are infinite points on its circumference, this means that a circle has an infinite number of diameters and each diameter ...
What is the radius of a circle?
The radius of the circle is half the diameter of the circle.
What is the formula for diameter?
The formula for diameter = 2√Area/π.
How many inches is a circle?
Answer: Diameter of the given circle = 48 inches.
What Is The Equation of A Circle?
Equation of A Circle When The Centre Is Origin
- Consider an arbitrary point P(x, y) on the circle. Let ‘a’ be the radius of the circle which is equal to OP. We know that the distance between the point (x, y) and origin (0,0)can be found using the distance formulawhich is equal to- √[x2+ y2]= a Therefore, the equation of a circle, with the center as the origin is, x2+y2= a2 Where “a” is the radius of the circle.
Equation of A Circle When The Centre Is Not An Origin
- Let C(h, k) be the centre of the circle and P(x, y)be any point on the circle. Therefore, the radius of a circle is CP. By using distance formula, (x-h)2 + (y-k)2 = CP2 Let radius be ‘a’. Therefore, the equation of the circle with center (h, k)and the radius ‘a’is, (x-h)2+(y-k)2 = a2 which is called the standard form for the equation of a circle.
General Form of Equation of A Circle
- The general equation of any type of circle is represented by: x2+y2+2gx+2fy+c = 0, for all values of g, f and c. Adding g2+f2on both sides of the equation gives, x2+2gx+g2+y2+2fy+f2= g2+f2−c………………(1) Since, (x+g)2 = x2+ 2gx + g2 and (y+f)2 =y2 + 2fy + f2substituting the values in equation (1), we …
Polar Equation of A Circle
- To find the polar form of equation of a circle, replace the value of x = r cos θ and y = r sin θ, in x2 + y2 = a2. Hence, we get; (r cos θ)2 + (r sin θ)2 = a2 r2 cos2 θ + r2 sin2 θ = a2 r2 (cos2 θ + sin2 θ) = a2 r2 (1) = a2[Using trigonometry identity] r = a is the polar equation of a circle with radius a and center at the origin (0,0).
How to Find The Equation of The Circle?
- To find the equation of a circle given the radius and center of the circle, we can directly put the values in the standard form of the equation. (x-h)2+ (y-k)2= r2 Here, some solved problems are given to find the equation of a circle in both cases such as when the center of a circle is origin and center is not an origin is given below.
Practice Questions on Equation of Circle
- Find the equation of a circle of radius 5 units, whose centre lies on the x-axis and which passes through the point (2, 3).
- Find the equation of a circle with the centre (h, k) and touching the x-axis.
- Show that the equation x2 + y2– 6x + 4y – 36 = 0 represents a circle. Also, find the centre and radius of the circle.