Question

If a number of ellipses whose major axis is $x$ -axis and the minor axis is $y$ -axis be described having the same length of the major axis as $2\,$ but a variable minor axis, then the tangents at the ends of their latus rectum pass through fixed points whose distance from the centre is equal to

• A. $\frac{1}{2}$ units
• B. $1$ unit
• C. $\frac{3}{2}$ units
• D. $2\,$ units

Answer 1

Answer: (B)

Since the minor axis is variable, hence $e$ is a variable quantity
Therefore the equation of the tangent to the ellipse can be written as $\frac{x a e}{a^{2}}+\frac{y b^{2}}{a b^{2}}=1$
$\Rightarrow ex+y=a\Rightarrow y-a+ex=0$
This line passes through the fixed point $\left(0 , a\right)$ (where $a=1$ )
Hence, distance from the centre of the ellipse $=1$