Q. Equation of chord of an ellipse $\frac{x^{2}}{25} + \frac{y^{2}}{9} = 1$, whose mid point is $(1,\ 1)$, is
A) $25x + 9y = 36$
B) $9x + 25y = 34$
C) $9x - 25y = 34$
D) None of these
Explanation
(b)
We know that, if $(x_{1},y_{1})$ is the mid point of the chord, then equation of chord is
$T = S_{1} \Rightarrow \frac{xx_{1}}{25} + \frac{yy_{1}}{9} = \frac{x_{1}^{2}}{25} + \frac{y_{1}^{2}}{9}$
$\because$ Point is $(1,\ 1)$, then
$\frac{x}{25} + \frac{y}{9} = \frac{1}{25} + \frac{1}{9}$
$\Rightarrow 9x + 25y = 34$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.