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Consider the parabola y^2=4xdot Let A-=(...

Consider the parabola `y^2=4xdot` Let `A-=(4,-4)` and `B-=(9,6)` be two fixed points on the parabola. Let `C` be a moving point on the parabola between `Aa n dB` such that the area of the triangle `A B C` is maximum. Then the coordinates of `C` are

A

(1/4,1)

B

(4,4)

C

`(3,2sqrt(3))`

D

`(3,-2sqrt(3))`

Text Solution

Verified by Experts

The correct Answer is:
A
(1) The area of triangle ABC is maximum if CD is maximum, because AB is fixed.
Therefore, the tangent drawn to the parabola at C should be parallel to AB.
Slope of AB `=(6+4)/(9-4)=2`
For `y^(2)=4x`,
`(dy)/(dx)=(2)/(y)=2`
`ory=1`
`orx=(1)/(4)`
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CENGAGE PUBLICATION-PARABOLA-EXERCISE (SINGLE CORRECT ANSWER TYPE )
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  15. If two different tangents of y^2=4x are the normals to x^2=4b y , then

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