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If the bisector of angle `A P B ,` where `P Aa n dP B` are the tangents to the parabola `y^2=4a x ,` is equally, inclined to the coordinate axes, then the point `P` lies on

A

tangent at vertex of the parabola

B

directrix of the parabola

C

circle with center at the origin and radius

D

the line of latus rectum

Text Solution

Verified by Experts

The correct Answer is:
D
(4)
Here, `(1)/(t_(1))="tan"((pi)/(4)+theta)`
`and(1)/(t_(2))="tan"((pi)/(4)-theta)`
So, `t_(1)t_(2)=1`
Therefore, the x-coordinate of P is `at_(1)t_(2),i.e.,a`.
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CENGAGE-PARABOLA-Exercise (Single)
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  2. If the locus of the middle of point of contact of tangent drawn to the...

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  3. If the bisector of angle A P B , where P Aa n dP B are the tangents to...

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  4. From a point A(t) on the parabola y^(2)=4ax, a focal chord and a tange...

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  5. The point of intersection of the tangents of the parabola y^(2)=4x dra...

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  6. The angle between the tangents to the parabola y^2=4a x at the points ...

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

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

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

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

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

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

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

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

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  15. The tangent at any point P onthe parabola y^2=4a x intersects the y-ax...

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

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

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

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

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  20. If 2x+y+lambda=0 is a normal to the parabola y^2=-8x , then lambda is ...

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