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The tangent at any point P onthe parabol...

The tangent at any point `P` onthe parabola `y^2=4a x` intersects the y-axis at `Qdot` Then tangent to the circumcircle of triangle `P Q S(S` is the focus) at `Q` is a line parallel to x-axis y-axis a line parallel to y-axis (d) none of these

A

a line parallel to axis

B

y-axis

C

a line parallel to y-axis

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
(2)
Tangent at P intersect the y-axis at `Q-=(0,at)`.
Also, circle with PS as diameter to touches the y-axis at (0,at).
So, the y-axis is the tangent to the circumcircle of `DeltaPQS` at Q.
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CENGAGE-PARABOLA-Exercise (Single)
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  4. If P(t^2,26),t in [0,2] , is an arbitrary point on the parabola y^2=4x...

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

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

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

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

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

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

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

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  13. If two different tangents of y^2=4x are the normals to x^2=4b y , then...

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  14. Maximum number of common normals of y^2=4ax and x^2=4by is

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

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

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

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

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  19. If the normals to the parabola y^2=4a x at the ends of the latus rectu...

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  20. From a point (sintheta,costheta), if three normals can be drawn to the...

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