# Conic Sections Equations

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Conic Section is defined as the intersection of a double right circular cone and a plane. The equation related to conic section is known as conic section equations. Basically the equation is represented as follows.

Ax^2+Bxy+C y^2+Dx+Ey+F = zero

There are basically four types of conic sections, which are as follows:-

1)      One is circles.

2)      Second is ellipses

3)      Third is hyperbolas and

4)      Last is a parabola.

In this conic section we will deal with circles equations, which are shown below:-

(x- h)^2 + (y-k) ^2 = r^2

Here h, k is the centre of circle and r is the radius of circle.

Now we will see some examples based on conic sections

Example 1: - Write down the equation of the following circle shown below. Here O is the center of circle and r is the radius of circle.

Solution: Given Center O (3, 4), so h = 3 and k = 4

=> Radius = 7 cm

=> We know that the equation of circle is:- (x- h)^2 + (y-k) ^2 = r^2

=> Therefore by substitution, we get (x- 3)^2 + (y-4) ^2 = 7^2

=> Therefore (x- 3) ^2 + (y-4) ^2 = 49 is the required equation of the circle.

Example 2:- Given center of circle is O (1, 2) and radius is 10 cm. Write down the equation of circle.

Solution: Given Center coordinates h = 1 and k = 2

=> Radius r = 10 cm.

=> We know that the equation of circle is:- (x- h)^2 + (y-k) ^2 = r^2

=> Therefore by substitution, we get (x- 1)^2 + (y-2) ^2 = 10^2

=> So (x- 1) ^2 + (y-2) ^2 = 100 is the required equation of the circle.