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

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-PARABOLA-Exercise (Single)
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  2. The mirror image of the parabola y^2=4x in the tangent to the parab...

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  3. Consider the parabola y^2=4xdot Let A-=(4,-4) and B-=(9,6) be two fixe...

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  6. If P(t^2,2t),t in [0,2] , is an arbitrary point on the parabola y^2=4x...

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  8. If the tangents and normals at the extremities of a focal chord of a ...

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  9. At what point on the parabola y^2=4x the normal makes equal angle with...

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  12. The equation of the line that passes through (10 ,-1) and is perpendic...

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  13. Tongent and normal drawn to a parabola at A(a t^2,2a t),t!=0 meet the ...

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  14. The radius of the circle touching the parabola y^2=x at (1, 1) and hav...

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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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  16. about to only mathematics

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  17. If line P Q , where equation is y=2x+k , is a normal to the parabola w...

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  18. min[(x1-x^2)^2+(3+sqrt(1-x1 2)-sqrt(4x2))],AAx1,x2 in R , is 4sqrt(5)...

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  19. If the normals to the parabola y^2=4a x at three points (a p^2,2a p), ...

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  20. Normals A O ,AA1a n dAA2 are drawn to the parabola y^2=8x from the poi...

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