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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)

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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CENGAGE-PARABOLA-Exercise (Comprehension)
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  6. If l and m are variable real number such that 5l^(2)+6m^(2)-4lm+3l=0, ...

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  7. Consider the parabola whose focus is at (0,0) and tangent at vertex is...

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  8. Consider the parabola whose focus is at (0,0) and tangent at vertex is...

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  9. Consider the parabola whose focus is at (0,0) and tangent at vertex is...

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  10. the tangent to a parabola are x-y=0 and x+y=0 If the focus of the para...

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  11. Two tangents on a parabola are x-y=0 and x+y=0. S(2,3) is the focus ...

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  12. Two tangents on a parabola are x-y=0 and x+y=0. S(2,3) is the focus ...

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  13. y^(2)=4xandy^(2)=-8(x-a) intersect at points A and C. Points O(0,0), A...

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  14. y^(2)=4xandy^(2)=-8(x-a) intersect at points A and C. Points O(0,0), A...

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  15. y^(2)=4xandy^(2)=-8(x-a) intersect at points A and C. Points O(0,0), A...

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  20. Consider the inequation 9^(x) -a3^(x) - a+ 3 le 0, where a is real p...

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