Test Index

Ellipse

Section: Mathematics

Question : 15 of 25

Marks: +1, -0

The ellipse

E_1

\frac{x^2}{9} + \frac{y^2}{4}

E_2

E_2

Solution:

The given situation is shown in the following figure:

Equation of ellipse is ( y + 2)( y - 2) + λ(x + 3)(x - 3) = 0.

It passes through (0,4) ⇒ λ =

\frac{4}{3}

Equation of ellipse is

\frac{x^2}{12} + \frac{y^2}{16}

= 1.

⇒ e =

\frac{1}{2}

Alternate solution: Let the ellipse be

\frac{x^2}{a^2} + \frac{y^2}{b^2}

= 1 as it is passing through (0, 4) and (3, 2).

So ,

b^2

= 16 and

\frac{9}{a^2} + \frac{4}{16}

⇒

a^2

= 12

So, 12 =

16(1-e^2)

⇒ e =

\frac{1}{2}

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