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

Question

The equation of tangent to the ellipse (x2/50)+(y2/32)=1 which passes through a point (15,-4) is (A) 4 x+5 y=40 (B) 4 x+35 y=200 (C) 4 x-5 y=40 (D) none of these

Tardigrade Admin · Accepted Answer

y+4=m(x-15) y=m x-(15 m+4) ....(1) for tangent (15 m+4)2=50 m2+32 175 m2+120 m-16=0 (35 m-4)(5 m+4)=0 m=(4/35), (-4/5) putting in (i) 4 x+5 y=40 and 4 x-35 y=200

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

$4 x + 5 y = 40$

$4 x + 35 y = 200$

$4 x - 5 y = 40$

none of these

$y + 4 = m (x - 15)$
$y = m x - (15 m + 4) ....$ (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 $4 x - 35 y = 200$

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

4x+5y=40

4x+35y=200

4x−5y=40