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Normal at the point `P(a p^2,2a p)` meets the parabola `y^2=4a x` again at `Q(a q^2,2a q)` such that the lines joining the origin to `Pa n dQ` are at right angle. Then, `P^2=2` (b) `q^2=2` `p=2q` (d) `q=2p`

A

`p^(2)+pq+2=0`

B

`p^(2)-pq+2=0`

C

`q^(2)+pq+2=0`

D

`p^(2)+pq+1=0`

Text Solution

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The correct Answer is:
A
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OBJECTIVE RD SHARMA ENGLISH-PARABOLA-Exercise
  1. If t is the parameter for one end of a focal chord of the parabola y^2...

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  2. Find the equation of normal to the parabola y^2=4axat point (at^2, 2at...

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  3. Normal at the point P(a p^2,2a p) meets the parabola y^2=4a x again at...

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  4. The length of the subnormal to the parabola y^(2)=4ax at any point is ...

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  5. The two parabolas y^(2)=4x" and "x^(2)=4y intersect at a point P, whos...

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  6. A set of parallel chords of the parabola y^2=4a x have their midpoint ...

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  7. Find the point on the curve y^(2)=ax the tangent at which makes an ang...

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

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  9. Find the angle at which the parabolas y^2=4x and x^2=32 y intersect.

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  10. The normal at (a,2a) on y^2 = 4ax meets the curve again at (at^2, 2at)...

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  11. If a chord which is normal to the parabola at one end subtend a right ...

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  12. Find the equations of the normals at the ends of the latus- rectum of ...

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  13. Normal at the point P(a p^2,2a p) meets the parabola y^2=4a x again at...

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  14. If the normals at points t1 and t2 meet on the parabola, then (a) t1...

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  15. If the normals at two points P and Q of a parabola y^2 = 4ax intersect...

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  16. Find the angle between the tangents drawn from the origin to the pa...

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  17. The angle between the tangents drawn from the point (-a, 2a) to y^2=4a...

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

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  19. P(-3, 2) is one end of focal chord PQ of the parabola y^2+4x+4y=0. The...

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  20. If x=my+c is a normal to the parabola x^(2)=4ay, then the value of c, ...

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