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y=x+2 is any tangent to the parabola y^2...

`y=x+2` is any tangent to the parabola `y^2=8xdot` The point `P` on this tangent is such that the other tangent from it which is perpendicular to it is `(2,4)` (b) `(-2,0)` `(-1,1)` (d) `(2,0)`

A

(2,4)

B

(-2,0)

C

(-1,1)

D

(2,0)

Text Solution

Verified by Experts

The correct Answer is:
B
(2) Clearly, P is the point of intersection of two perpendicular tangents to the parabola `y^(2)=8x`.
Hence, P must lie on the directrix x+a=0orx+2=0.
Therefore, x=-2.
Hence, the point is (-2,0).
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CENGAGE-PARABOLA-Exercise (Single)
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  11. The tangent at any point P onthe parabola y^2=4a x intersects the y-ax...

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  12. If P(t^2,26),t in [0,2] , is an arbitrary point on the parabola y^2=4x...

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  13. The minimum area of circle which touches the parabolas y=x^(2)+1andy^(...

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

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  16. The line 2x+y+lamda=0 is a normal to the parabola y^(2)=-8x, is lamda=

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  17. If two normals to a parabola y^2 = 4ax intersect at right angles then ...

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

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

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

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