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In parabola y^2=4x, From the point (15,1...

In parabola y^2=4x, From the point (15,12), three normals are drawn to the three co-normals point is

A

(16/3.0)

B

(4,0)

C

(26/3.0)

D

(6,0)

Text Solution

Verified by Experts

The correct Answer is:
C
(3) Let the equation of any normal be `y=-tx+2t+t^(3)`.
Since it passes through the point (15,12) we have
`12=-15t+2t+t^(3)`
`ort^(3)-13t-12=0`
One root is -1. Then,
`(t+1)(t^(2)-t-12)=0`
`ort=-1,-3,4`
Therefore, the co-normal points are (1,-2), (9,-6), and (16,8).
Therefore, the centroid is (26/3,0).
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