Question

If a number of the ellipse (whose axes are $x$ and $y$ axes) be described having the same major axis $2a$ but a variable minor axis then the tangents at the end of their latus rectum pass through fixed points which can be

• A. (0,a) and (0,-a)
  
• B. 1
• C. 2
• D. 3

Answer 1

The correct option is A (0,a) and (0,-a)

Equation of the ellipse is

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

$x$ axis is the major axis

Latus rectum co-efficient

$(ae,\frac{b^2}{a})$

Equation of tangent

$\pm \frac{x}{a^2}aP\pm \frac{y}{b^2}.\frac{b^2}{a}=1\frac{P^x}{a}+\frac{y}{a}-1=0Px+y-a=0(y-a)+Px=0L_1+\lambda L_2=0y=ax=0$

So, $(0,a)$ and $(0,-a)$