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The angle between the tangents to the pa...

The angle between the tangents to the parabola `y^2=4a x` at the points where it intersects with the line `x-y-a=0` is (a)`pi/3` (b) `pi/4` (c) `pi` (d) `pi/2`

A

`pi//3`

B

`pi//4`

C

`pi//6`

D

`pi//2`

Text Solution

Verified by Experts

The correct Answer is:
D
(4) The coordinates of the focus of the parabola `y^(2)=4ax` are (a,0).
the line y-x-a=0 passes through this point. Therefore, it is a focal chord of the parabola. Hence, the tangent intersects at right angle.
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CENGAGE-PARABOLA-Exercise (Single)
  1. From a point A(t) on the parabola y^(2)=4ax, a focal chord and a tange...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  18. about to only mathematics

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

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

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