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The slope of the line touching both the ...

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

A

`1//2`

B

`3//2`

C

`1//8`

D

`2//3`

Text Solution

Verified by Experts

The correct Answer is:
A
1 Equation of tangent to `y^(2)=4x` at A `(t^(2),2t)` is
`yt=x+t^(2)`
This is tangent to `x^(2)+32=0`
`rArrx^(2)+32((x)/(t)+t)=0rArrx^(2)+(32)/(t)x+32t=0`
Above equation must have eqaution roots
`rArr((32)/(t))^(2)-4(32t)=0`
`rArr32((32)/(t^(2))-4t)=0`
`rArrt^(3)=8rArrt=2`
`rArr" Slope of tangent is "(1)/(t)=(1)/(2)`.
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