Question

If lines x - y + 2 = 0 and 2x - y - 2 = 0 meet at 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. 3 x - y- 16 = 0
• D. x - 3y + 16 = 0

Answer 1

The correct option is A x - 2y + 8 = 0

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