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Find the equations of the normals at the...

Find the equations of the normals at the ends of the latus- rectum of the parabola `y^2= 4ax.` Also prove that they are at right angles on the axis of the parabola.

A

`x^(2)-y^(2)-6ax+9a^(2)=0`

B

`x^(2)-y^(2)-6ax-6ay+9a^(2)=0`

C

`x^(2)-y^(2)-6xy+9a^(2)=0`

D

none of these

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The correct Answer is:
A
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OBJECTIVE RD SHARMA ENGLISH-PARABOLA-Exercise
  1. The normal at (a,2a) on y^2 = 4ax meets the curve again at (at^2, 2at)...

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

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

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

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

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

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

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

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

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

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

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  12. Find the equations of the tangent to the given curve at the indicated...

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  13. The tangents at the points (at(1)^(2), 2at(1)), (at(2)^(2), 2at(2)) on...

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  14. If the vertex of the parabola y=x^(2)-8x+c lies on x-axis, then the va...

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  15. If the chord y = mx + c subtends a right angle at the vertex of the p...

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  16. The equation of the tangent at the vertex of the parabola x^(2)+4x+2y=...

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  17. The locus of the point of intersection of the perpendicular tangents t...

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  18. If y=2x+3 is a tangent to the parabola y^2=24 x , then find its distan...

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  19. If the normal at(1, 2) on the parabola y^(2)=4x meets the parabola aga...

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  20. The normals at three points P,Q,R of the parabola y^2=4ax meet in (h.k...

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