Question

2. Determine the equation of the ellipse with the center (0,0), major vertices (-6,0) and (6,0,) and foci (-4,0) and (4,0)

Answer 1

Given

Vertices (-6,0) and (6,0) , Foci (-4,0) and (4,0)........(1)

The vertices are of the form (+a,0) and (-a,0).........(2)

Hence the major axis along x axis and equation of ellipse is of the form

$\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1$

From (1) and (2)

a=6

Also given coordinate of foci (4,0) and (-4,0)

We know that foci = (+c,0) and (-c,0)

c=4

We know that

62 = 20

Equation of ellipse is

$\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1$

Putting values

$\frac{x^{2}}{36}+\frac{y^{2}}{20}=1$