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The tangent to the curve y=x^2-5x+5. par...

The tangent to the curve `y=x^2-5x+5.` parallel to the line `2y=4x+1,` also passes through the point :

A

`((7)/(2), (1)/(4))`

B

`((1)/(8), -7)`

C

`((1)/(4), (7)/(2))`

D

`(-(1)/(8), 7)`

Text Solution

Verified by Experts

The correct Answer is:
B
Tangent is parallel to `y = 2x + (1)/(2)`
So slope will be 2
Let equation is `y = 2x + c` solve it with curv will give only one solution
`2x + c = x^(2) - 5x + 5 rArr x^(2) - 7x + 5 - c = 0`
Put D = 0
`(-7)^(2) -4(5-c) = 0 rArr (49)/(4) = 5 - c rArr c = 5 - (49)/(4) = (-29)/(4)`
`y = 2x - (29)/(4)`, so `[(1)/(8), -7]` will satisfy
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