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Show that the tangents to the curve `y=x^2-5x+6` at the point (2,0) and (3,0) are at right angle.

A

`(pi)/(2)`

B

`(pi)/(3)`

C

`(pi)/(6)`

D

`(pi)/(4)`

Text Solution

Verified by Experts

The correct Answer is:
A
(1) `(dy)/(dx)=2x-5`
`:." "m_(1)=((dy)/(dx))_((2","0))=4-5=-1`
`and" "m_(2)=((dy)/(dx))_((3","0))=6-5=1`
`:." "m_(1)m_(2)=-1`
Therefore, the angle between the tangents is `pi//2`.
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CENGAGE PUBLICATION-PARABOLA-EXERCISE (SINGLE CORRECT ANSWER TYPE )
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  20. The equation of the common tangent to the parabolas y^2= 4ax and x^2=...

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