Conic Section Formulas

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Conic Section formulas are basically the formulas of ellipse, circle, hyperbola and parabola. All of these have

separate equations. For understanding the conic section formulas, one shall understand the basic concepts

of ellipse, circle, hyperbola and parabola.

For understanding purpose we can take one conic section example.

The conic section formula of circle is as follows:-

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

Here h, k are the centers of the circle

And r is the radius of circle.

Still for better understanding, some of the examples given below:-


Example 1:- Write down the equation of circle if the centers are (90, 100) and diameter of circle is

10 cm.



Solution: Given Center (h, k) is (90, 100)

 That is h = 90 and k = 100

 Also given the diameter of circle = 10 cm

 We know that, Radius of circle = Diameter of circle/2 = 10/2 = 5 cm

 Now we also know that the equation of circle is

 (x- h)^2 + (y-k) ^2 = r ^2

 So by substitution method,

 (x- 90)^2 + (y- 100) ^2 = 5 ^2

 Hence (x- 90) ^2 + (y- 100) ^2 = 25 is the required equation of the circle.

 
Example 2:- Write down the equation of circle if the centers are (100, 200) and diameter of circle is

20 cm.



Solution: Given Center (h, k) is (100, 200)

 That is h = 100 and k = 200

 Also given the diameter of circle = 20 cm

 We know that, Radius of circle = Diameter of circle/2 = 20/2 = 10 cm

 Now we also know that the equation of circle is

 (x- h)^2 + (y-k) ^2 = r ^2

 So by substitution method,


 (x- 100)^2 + (y- 200) ^2 = 10 ^2

 Hence (x- 100)^2 + (y- 200) ^2 = 100 is the required equation of the circle.





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