Home
Class 12
MATHS
The normal to the parabola y^(2)=4ax at ...

The normal to the parabola `y^(2)=4ax` at three points P,Q and R meet at A. If S is the focus, then prove that `SP*SR=aSA^(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
Promotional Banner

Topper's Solved these Questions

  • PARABOLA

    ARIHANT MATHS ENGLISH|Exercise Exercise (More Than One Correct Option Type Questions)|14 Videos

  • PARABOLA

    ARIHANT MATHS ENGLISH|Exercise Exercise (Passage Based Questions)|24 Videos

  • PARABOLA

    ARIHANT MATHS ENGLISH|Exercise Exercise For Session 2|25 Videos

  • PAIR OF STRAIGHT LINES

    ARIHANT MATHS ENGLISH|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|2 Videos

  • PERMUTATIONS AND COMBINATIONS

    ARIHANT MATHS ENGLISH|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|28 Videos

Similar Questions

Explore conceptually related problems

If the normals to the parabola y^2=4a x at three points P ,Q ,a n dR meet at A ,a n dS is the focus, then S PdotS qdotS R is equal to a^2S A (b) S A^3 (c) a S A^2 (d) none of these

The normal to parabola y^(2) =4ax from the point (5a, -2a) are

The tangents to the parabola y^2=4a x at the vertex V and any point P meet at Q . If S is the focus, then prove that S PdotS Q , and S V are in GP.

The tangents to the parabola y^2=4a x at the vertex V and any point P meet at Q . If S is the focus, then prove that S PdotS Q , and S V are in GP.

The normal to the parabola y^(2)=8ax at the point (2, 4) meets the parabola again at the point

The normal to the parabola y^(2)=8x at the point (2, 4) meets the parabola again at eh point

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 .

The normal chord of a parabola y^2= 4ax at the point P(x_1, x_1) subtends a right angle at the

If the normal to the parabola y^2=4ax at the point (at^2, 2at) cuts the parabola again at (aT^2, 2aT) then

Tangent PT and normal PN to the parabola y^(2)=4ax at a point P on it meet its axis at T and N respectively. The Locus of the centroid of the triangle PTN is a parabola whose

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

    Text Solution

    |

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

    Text Solution

    |

  3. The normal to the parabola y^(2)=4ax at three points P,Q and R meet at...

    Text Solution

    |

  4. about to only mathematics

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  9. Normals at two points (x1y1)a n d(x2, y2) of the parabola y^2=4x meet ...

    Text Solution

    |

  10. A line is drawn form A(-2,0) to intersect the curve y^2=4x at Pa n dQ ...

    Text Solution

    |

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

    Text Solution

    |

  12. C is the center of the circle with center (0, 1) and radius unity. P i...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  18. If the fourth term in the expansion of (a x+1/x)i s5/2,\ then find th...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |