# Conic Section ellipse

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Here center is (h, k) and above equations is the basic part of the conic section ellipse.

Conic section ellipse can be clearly understood by the following examples:-

Example 1: For a conic section ellipse equation with the coefficients is (25 x^2) + (16 y^2) = 400. What will be a and b?

Solution: In the given problem

(25 x^2) + (16 y^2) = 400 (divide the equation by 400)

(25 x^2)/400 + (16 y^2)/400 = 400/400 (When we rearrange the equation)

X^2 / (400/25) + y^2 / (400/16) = 1 (Now according to the ellipse equation)

a^2 = 400/25, a = 20/5 = 4

b^2 = 400/16, b = 20/4 = 5

Example 2: For a conic section ellipse a = 6 and b = 7 and x = 2. Find y from the equation.

Solution: In the given problem

X^2/ a^2 + y^2 / b^2 = 1 (plugging in the values)

2^2/ 6^2 + y^2 / 7^2 = 1

4/36 + y^2 / 49 = 1

y^2 / 49 = 1 – 4/36

y^2 = (32 / 36) x 49

y^2 = 43.55, y = 6.59