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

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

Conic Sections

Solution:

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