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Q.
If $3 x+4 y=12$ intersect the ellipse $\frac{x^2}{25}+\frac{y^2}{16}=1$ at $P$ and $Q$, then the point of intersection of tangents at $P$ and $Q$ is
Conic Sections
Solution:
Let point of intersection is $R(h, k)$
$P Q$ is chord of contact
$\frac{ hx }{25}+\frac{ ky }{16}=1 .....$(i)
equation $ \frac{x}{4}+\frac{y}{3}=1......$(ii)
Comparing (i) and (ii)
$\Rightarrow $ equation $ \frac{ h }{25}=\frac{1}{4}, k =\frac{16}{3}$