Question

An ellipse, with foci at (0, 2) and (0, –2) and minor axis of length 4, passes through which of the following points?
(A) (2, √2) (B) (2, 2√2)
(C) (1, 2√2) (D) (√2, 2)

Answer 1

(√2, 2) lies on ellipse.

•let equation of ellipse will be

x²/a² + y²/b² = 1 ; a² = b²(1-e²)

where e is ecentricity

A•Given,

ellipse with foci at (0, 2) and (0, –2)

clearly, it's major axis is Y axis

•so, Minor axis will be Xaxis

• length of minor axis = 2a

4 = 2a

a = 2 ______(1)

•Also, for ellipse with major axis as Y axis

focii lie on (0 ,be) & (0,-be)

•Now, focii of ellipse is at (0,2)&(0,-2)

be = 2 ______(2)

•Also a² = b²(1-e²)

a² = b²-b²e²

4 = b²-4

b² = 8 ______(3)

As, b² = 8 & a² = 4

•Equation of ellipse will be ;

x²/4 + y²/8 = 1

So, by putting all the coordinates in equation we found, (√2, 2) lies on ellipse.