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y=x is tangent to the parabola y=ax^(2)+...

y=x is tangent to the parabola `y=ax^(2)+c`.
If c=2, then the point of contact is (a) (3,3) (b) (2,2) (c) (6,6) (d) (4,4)

A

(3,3)

B

(2,2)

C

(6,6)

D

(4,4)

Text Solution

Verified by Experts

The correct Answer is:
D
(4) If c=2, then the point of contact is `(1//2a,1//4a+2)`.
Since it lies on the line y=x, we have
`(1)/(2a),(1)/(4a)+2`
`i.e," "a=(1)/(8)`
Therefore, the point of contact is (4,4)
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