Question

What is an equation in standard form of an ellipse centered at the origin with vertex (-5 0) and co-vertex (0 -3?

Answer 1

x^2/25 + y^2/9 = 1

Explanation:

Answer 2

The general equation of the ellipse is

`( (x-h)^(2) )/( a^(2) ) + ( (y-k)^(2) )/( b^(2) ) =1`
where (h,k) the coordinates of the center
a and b represents half the length of the axes

given: center of the ellipse = (0,0)
vertex (-5 , 0) and co-vertex (0 , -3)
∴ (h,k) = (0,0)
∴ a = 5 and b = 3
So, The equation in standard form of the ellipse is


`( x^(2) )/( 25 ) + ( y^(2) )/( 9 ) =1`