Question

Please help me write an equation?

Answer 1

1. `x^2/49+y^2/4=1`
2. `x^2/169+y^2/25=1`

Explanation:

1. As center is `0,0)` and one vertex is `(-7,0)` other vertex would be `(7,0)` and hence major axis is `14` i.e. in standard equation `a=7`. Similarly as one co-vertex is `(0,2)`, other co-vertex is `(0,-2)` and minor axis is `4` and `b=2`. The equation is

`x^2/7^2+y^2/2^2=1` or `x^2/49+y^2/4=1`

graph{x^2/49+y^2/4=1 [-10, 10, -5, 5]}

1. As center is `(0,0)` and one vertex is `(13,0)`, other vertex `(-13,0)` and `a=13`. As one focus is `(-12,0)`, we have `ae=12` and as `a=13`, eccentricity is `12/13`

and `b=asqrt(1-e^2)=13sqrt(1-(12/13)^2)=sqrt(13^2-12^2)=5`

and equation of ellipse is

`x^2/169+y^2/25=1`

graph{(x^2/169+y^2/25-1)((x+12)^2+y^2-0.05)((x-12)^2+y^2-0.05)=0 [-14, 14, -7, 7]}