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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 (a)`(2,4)` (b) `(-2,0)` (c)`(-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 ENGLISH-PARABOLA-EXERCISE (SINGLE CORRECT ANSWER TYPE )
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  2. The angle between tangents to the parabola y^2=4ax at the points where...

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  3. y=x+2 is any tangent to the parabola y^2=8xdot The point P on this tan...

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  4. If y=m1x+c and y=m2x+c are two tangents to the parabola y^2+4a(x+c)=0 ...

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  5. The angle between the tangents to the curve y=x^2-5x+6 at the point (2...

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  6. Two mutually perpendicular tangents of the parabola y^(2)=4ax meet the...

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  7. Radius of the circle that passes through the origin and touches the ...

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  8. The mirror image of the parabola y^2= 4x in the tangent to the parabol...

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

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  10. A line of slope lambda(0 < lambda < 1) touches the parabola y+3x^2=0 a...

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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^2,2t),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+1 and y^2...

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

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

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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. about to only mathematics

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

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  19. Tangent 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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