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The point of intersection of the tangents of the parabola `y^(2)=4x` drawn at the end point of the chord x+y=2 lies on

A

x-2y=0

B

x+2y=0

C

y-x=0

D

x+y=0

Text Solution

Verified by Experts

The correct Answer is:
C
(3) Let the point of intersection be `(alpha,beta)`.
Therefore, the chord of contact w.r.t. this point is
`betay=2x+aalpha`
which is the same as x+y=2. Therefore,
`alpha=beta=-2`
These value satisfy y-x=0.
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CENGAGE-PARABOLA-Exercise (Single)
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  3. The point of intersection of the tangents of the parabola y^(2)=4x dra...

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  4. The angle between tangents to the parabola y^2=4ax at the points where...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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