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  4. The equation of tangent to the ellipse (x2/50)+(y2/32)=1 which passes through a point (15,-4) is

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Q. The equation of tangent to the ellipse $\frac{x^2}{50}+\frac{y^2}{32}=1$ which passes through a point $(15,-4)$ is

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Solution:

$y+4=m(x-15)$
$y=m x-(15 m+4) ....$(1)
for tangent
$(15 m+4)^2=50 m^2+32$
$175 m^2+120 m-16=0$
$(35 m-4)(5 m+4)=0$
$m=\frac{4}{35}, \frac{-4}{5}$
putting in (i)
$4 x+5 y=40$
and $4 x-35 y=200$