Question

Equation of a tangent to the parabola $y^2=12 x$ which make an angle of $45^{\circ}$ with line $y=3 x+77$ is

• A. $2 x-4 y+3=0$
• B. $x+2 y+12=0$
• C. $4 x+2 y+3=0$
• D. $2 x+y-12=0$

Answer 1

Answer: (C)

Let the equation of tangent is $y=m x+\frac{a}{m}$
$y=m x+\frac{3}{m} $
$\tan 45^{\circ}=\left|\frac{m-3}{1+3 m}\right| $
$\Rightarrow \frac{m-3}{1+3 m}=\pm 1 $
$\Rightarrow 4 m-2=0 \& 2 m+4=0$
$\Rightarrow m=\frac{1}{2} \&-2$
$\therefore$ equation of tangents
$y=-2 x-\frac{3}{2} \& y=\frac{1}{2} x+6 $
$2 y=-4 x-3 \& 2 y=x+12$