The slope of the line touching both the parabolas `y^2=4x and x^2=−32y` is

Options

A. 43473
B. 43499
C. 43467
D. 43526

Answer

C

Explanation

The equation of any tangent to `y^(2)=4x` is `y=mx+1/m"or, "x=1/my-1/m^(2)`. If it touches `x^(2)=-32y,` then As the equation of any tangent to `x^(2)=-32y`, is of the form `x=my-8/m.`
`:." "-1/m^(2)=-8/("1/m")rArrm=1/2`
ALITER The equation of any tangent to `y^(2)=4x" is "y =mx+1/m`. If it touches `x^(2)=-32y," then "x^(2)=-32(mx+1/2)` must have equal roots.
`:." "(32m)^(2)=4((32)/(m))rArr=m=1/2`