Question

The equation of the ellipse having foci (2, 0), ( -2, 0) and minor axis of length 8 units is:

1. \(\rm \frac{x^2}{16}+\frac{y^2}{20}=1\)
2. \(\rm \frac{x^2}{20}+\frac{y^2}{16}=1\)
3. \(\rm \frac{x^2}{2\sqrt5}+\frac{y^2}{4}=1\)
4. \(\rm \frac{x^2}{4}+\frac{y^2}{2\sqrt5}=1\)

Answer 1

Correct Answer - Option 2 : \(\rm \frac{x^2}{20}+\frac{y^2}{16}=1\)

Concept:

The distance between the centre and the focus of an ellipse is c = ae

The equation of an ellipse with the length of the major axis 2a and the minor axis 2b is given by: \(\rm \frac{x^2}{a^2}+\frac{y^2}{b^2}=1\).

 

Calculation:

Length of the minor axis = 2b = 8.

⇒ b = 4.

Also, c = distance between the centre and the focus = ae = 2.

c2 = a2e2 = a2 - b2

∴ 22 = a2 - 42

⇒ a² = 20

Equation of the ellipse = \(\rm \frac{x^2}{a^2}+\frac{y^2}{b^2}=1\).

⇒ \(\rm \frac{x^2}{20}+\frac{y^2}{16}=1\).