# How do you find the equation in standard form of an ellipse that passes through the given points: (5, 6), (5, 0), (7, 3), (3, 3)?

##### 1 Answer

Equation of ellipse is

#### Explanation:

Let the equation of the ellipse be

As it passes through

**.....(A)**

**.....(B)**

Subtracting (B) from (A) we get

i.e.

**.....(C)**

**.....(D)**

Subtracting (D) from (C) we get

i.e.

This reduces the equations (A) and (C) to

and

Hence, the equation of ellipse is

and ellipse appears as one shown below

graph{((x-5)^2/4+(y-3)^2/9-1)((x-5)^2+(y-6)^2-0.02)((x-5)^2+y^2-0.02)((x-7)^2+(y-3)^2-0.02)((x-3)^2+(y-3)^2-0.02)=0 [-5.71, 14.29, -2.48, 7.52]}