Home
Class 12
MATHS
The tangent at any point P onthe parabol...

The tangent at any point `P` onthe parabola `y^2=4a x` intersects the y-axis at `Qdot` Then tangent to the circumcircle of triangle `P Q S(S` is the focus) at `Q` is

A

a line parallel to axis

B

y-axis

C

a line parallel to y-axis

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
(2)
Tangent at P intersect the y-axis at `Q-=(0,at)`.
Also, circle with PS as diameter to touches the y-axis at (0,at).
So, the y-axis is the tangent to the circumcircle of `DeltaPQS` at Q.
Promotional Banner

Topper's Solved these Questions

  • PARABOLA

    CENGAGE PUBLICATION|Exercise EXERCISE (MULTIPLE CORRECT ANSWER TYPE )|26 Videos

  • PARABOLA

    CENGAGE PUBLICATION|Exercise LINKED COMPREHENSION TYPE|45 Videos

  • PARABOLA

    CENGAGE PUBLICATION|Exercise Concept Applications Exercise 5.7|9 Videos

  • PAIR OF STRAIGHT LINES

    CENGAGE PUBLICATION|Exercise Numberical Value Type|5 Videos

  • PERMUTATION AND COMBINATION

    CENGAGE PUBLICATION|Exercise Comprehension|8 Videos

Similar Questions

Explore conceptually related problems

If a tangent to the parabola y^2=4a x meets the x-axis at T and intersects the tangents at vertex A at P , and rectangle T A P Q is completed, then find the locus of point Qdot

If the tangent at any point P to the parabola y^(2)=4ax meets the directrix at the point K , then the angle which KP subtends at its focus is-

If the tangent at the point P(2,4) to the parabola y^2=8x meets the parabola y^2=8x+5 at Qa n dR , then find the midpoint of chord Q Rdot

Tangents PA and PB are drawn to x^2+y^2=a^2 from the point P(x_1, y_1)dot Then find the equation of the circumcircle of triangle P A Bdot

A tangent is drawn to the parabola y^2=4a x at P such that it cuts the y-axis at Qdot A line perpendicular to this tangents is drawn through Q which cuts the axis of the parabola at R . If the rectangle P Q R S is completed, then find the locus of Sdot .

Tangent is drawn at any point (p ,q) on the parabola y^2=4a xdot Tangents are drawn from any point on this tangant to the circle x^2+y^2=a^2 , such that the chords of contact pass through a fixed point (r , s) . Then p ,q ,r and s can hold the relation (a) r^2q=4p^2s (b) r q^2=4p s^2 (c) r q^2=-4p s^2 (d) r^2q=-4p^2s

If two tangents drawn from a point P to the parabola y^2 = 4x are at right angles, then the locus of P is

If the tangents at the points Pa n dQ on the parabola y^2=4a x meet at T ,a n dS is its focus, the prove that S P ,S T ,a n dS Q are in GP.

A straight line through the vertex P of a triangle P Q R intersects the side Q R at the points S and the cicumcircle of the triangle P Q R at the point Tdot If S is not the center of the circumcircle, then 1/(P S)+1/(S T) 2/(sqrt(Q SxxS R)) 1/(P S)+1/(S T) 4/(Q R)

If a tangent to the parabola y^2 = 4ax intersects the x^2/a^2+y^2/b^2= 1 at A and B , then the locus of the point of intersection of tangents at A and B to the ellipse is

CENGAGE PUBLICATION-PARABOLA-EXERCISE (SINGLE CORRECT ANSWER TYPE )
  1. Consider the parabola y^2=4xdot Let A-=(4,-4) and B-=(9,6) be two fixe...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  5. The minimum area of circle which touches the parabolas y=x^2+1 and y^2...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  9. about to only mathematics

    Text Solution

    |

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

    Text Solution

    |

  11. Tangent and normal drawn to a parabola at A(a t^2,2a t),t!=0 meet the ...

    Text Solution

    |

  12. The radius of the circle touching the parabola y^2=x at (1, 1) and hav...

    Text Solution

    |

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

    Text Solution

    |

  14. The equation of the common tangent to the parabolas y^2= 4ax and x^2=...

    Text Solution

    |

  15. If line P Q , where equation is y=2x+k , is a normal to the parabola w...

    Text Solution

    |

  16. Evaluate, min[(x1-x2)^2+(5+sqrt(1-x1^2)-sqrt(4x2))^2],AAx1,x2 in R , ...

    Text Solution

    |

  17. If the normals to the parabola y^2=4a x at three points (a p^2,2a p), ...

    Text Solution

    |

  18. Normals A O ,A A1a n dA A2 are drawn to the parabola y^2=8x from the p...

    Text Solution

    |

  19. If the normals to the parabola y^2=4a x at the ends of the latus rectu...

    Text Solution

    |

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

    Text Solution

    |