Question

the equation of ellipse whose one of the vertices is (0, +-7) and foci (0, +-3)​

Answer 1

Answer:

Equation of the ellipse with vertices (0,±17) and foci (0,±8) is:

Step-by-step explanation

225x2​+289y2​=1

Given,Vertices (0,+​17) and foci (0,+​8),so center of ellipse will be (0,0)

As foci are on y-axis,major axis will be y-axis

Let ,2b and 2a be lengths of major and minor axis respectively and e be eccentricity of ellipse.

Now ,length of major axis will be form vertices,2b=34

We know that ,distance between foci is 2be,then e=178​

and also we know that b2(1−e2)=a2⟹a2=225

Then equation of ellipse will be a2x2​+b2y2​=1⟹225x2​+289y2​=1