Question

If lines $x-y+2=0$ and $2x-y-2=0$ meet at a point $P$ then equation of tangent drawn to the parabola $y^2=8x$ from the point ' $P$ ' is

• A. $x-2y+8=0$
• B. $x+y-16=0$
• C. $3x-y-16=0$
• D. $x-3y+16=0$

Answer 1

Answer: (A)

St. line passing through $(4,6)$
$y-6=m(x-4)$
$y=mx+6-4m\text{ which is tangent to the parabola }{y}^2=8x$
$\therefore 6-4m=\frac{2}{m}\Rightarrow 3m-2m^2=1$
$\Rightarrow 2m^2-3m+1=0\Rightarrow m=\frac{1}{2},1$
$y=\frac{1}{2}x+6-2\Rightarrow 2y=x+8$
$x-2y+8=0$