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If the normals at P, Q, R of the parabol...

If the normals at P, Q, R of the parabola `y^2=4ax` meet in O and S be its focus, then prove that `.SP . SQ . SR = a . (SO)^2`.

A

`(SA)^2`

B

`(SA)^3`

C

`a(SA)^2`

D

`a(SA)^3`

Text Solution

Verified by Experts

The correct Answer is:
C
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ARIHANT MATHS-PARABOLA-Exercise (Single Option Correct Type Questions)
  1. Two mutually perpendicular tangents of the parabola y^(2)=4ax meet the...

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  2. If the normals to the parabola y^2=4a x at P meets the curve again at ...

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  3. If the normals at P, Q, R of the parabola y^2=4ax meet in O and S be...

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  4. Length of the shortest normal chord of the parabola y^2=4ax is

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  5. The largest value of a for which the circle x^2 +y^2 = a^2 falls total...

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

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

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  8. The shortest distance between the parabolas 2y^2=2x-1 and 2x^2=2y-1 is...

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  9. Normals at two points (x1,x2) and (x2,y2) of the parabola y^2=4x meet ...

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  10. A line is drawn from A(-2,0) to intersect the curve y^2 = 4x in P and ...

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  11. An equilateral triangle SAB in inscribed in the parabola y^2 = 4ax hav...

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  12. C is the centre of the circle with centre (0,1) and radius unity. y=ax...

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  13. Let S be the focus of y^2=4x and a point P be moving on the curve such...

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  14. If P be a point on the parabola y^2=3(2x-3) and M is the foot of perpe...

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

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  16. Through the vertex O of the parabola y^2=4a x , two chords O Pa n dO Q...

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  17. A B is a double ordinate of the parabola y^2=4a xdot Tangents drawn to...

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  18. If the fourth term in the expansion of (px+1/x)^n is 5/2, then (n,p)...

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  19. The set of points on the axis of the parabola y^2-4x-2y+5=0 from which...

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  20. The tangent to the parabola y=x^2 has been drawn so that the abscissa ...

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