Conic Sections Equations

Conic Sections Equations 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.