Question

If the line $25x+12y-45=0$ meets the hyperbola $25x^2-9y^2=225$ only at point $(a,-\frac{5\lambda }{3}),$ then the value of $a+\lambda$ is

Answer 1

The equation ofgiven line is $25x+12y-45=0,$
$\Rightarrow y=-\frac{25}{12}x+\frac{15}{4}$
$\because$ point of contact is
$(-\frac{a^{2}m}{c},-\frac{b^2}{c})\equiv (5,-\frac{20}{3})\therefore -\frac{5\lambda }{3}=-\frac{20}{3}\Rightarrow \lambda =4,a=5$