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.
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.
