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Equation of common tangent of y=x^2,y=-...

Equation of common tangent of `y=x^2,y=-x^2+4x-4` is

A

y = 4 (x - 1)

B

y = 0

C

y = - 4(x - 1)

D

y = - 30x - 50

Text Solution

Verified by Experts

The correct Answer is:
A, B
The equation of tangent to `y = x^(2)`, be `y = mx - (m^(2))/(4)`
Putting in `y = - x^(2) +4 x - 4` we should only get one value of x i.e., Discrimunant must be zero.
`:.mx - (m^(2))/(4) = - x^(2) + 4x - 4`
`implies x^(2) + x (m - 4) + 4 - (m^(4))/(4) = 0`
Now, `(m - 4)^(2) - (16 - m^(2)) = 0`
`implies 2m (m - 4) = 0 implies m = 0,4`
`:.` y = 0 and y = 4 (x - 1) are the requried tangents.
Hence, (a) and (b) are correct answers.
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