Home
Class 12
MATHS
Tangent and normal are drawn at P(16,16)...

Tangent and normal are drawn at P(16,16) on the parabola `y^2=16x` which intersect the axis of the parabola at A and B respectively. If C is the centre of the circle through the points P,A and B and `angle CPB=theta` then the value of `tan theta` is

A

`4/3`

B

`1/2`

C

2

D

3

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • PARABOLA

    MOTION|Exercise EXERCISE - III|25 Videos

  • MONOTONOCITY

    MOTION|Exercise Exercise - 4 ( Level-II ) Previous Year (Paragraph)|2 Videos

  • PERMUTATION AND COMBINATION

    MOTION|Exercise EXAMPLE|23 Videos

Similar Questions

Explore conceptually related problems

Tangent and normal are drawn at the point P-=(16 ,16) of the parabola y^2=16 x which cut the axis of the parabola at the points Aa n dB , rerspectively. If the center of the circle through P ,A ,a n dB is C , then the angle between P C and the axis of x is (a)tan^(-1)(1/2) (b) tan^(-1)2 (c)tan^(-1)(3/4) (d) tan^(-1)(4/3)

A tangent and a normal are drawn at the point P(8, 8) on the parabola y^(2)=8x which cuts the axis of the parabola at the points A and B respectively. If the centre of the circle through P, A and B is C, then the sum f sin(anglePCB) and cot(anglePCB) is equal to

The tangent and normal at the point p(18, 12) of the parabola y^(2)=8x intersects the x-axis at the point A and B respectively. The equation of the circle through P, A and B is given by

The tangent and normal at the point P(4,4) to the parabola, y^(2) = 4x intersect the x-axis at the points Q and R, respectively. Then the circumcentre of the DeltaPQR is

For the parabola y^(2)=8x tangent and normal are drawn at P(2.4) which meet the axis of the parabola in A and B .Then the length of the diameter of the circle through A,P,B is

A tangent and a normal are drawn at the point P(2,-4) on the parabola y^(2)=8x , which meet the directrix of the parabola at the points A and B respectively. If Q (a,b) is a point such that AQBP is a square , then 2a+b is equal to :

Normals are drawn at points P, Q are R lying on the parabola y^(2)=4x which intersect at (3, 0), then

Normals are drawn at points A,B, and C on the parabola y^(2)=4x which intersect at P.The locus of the point P if the slope of the line jocuing the feet of two of them is 2, is

MOTION-PARABOLA-EXERCISE - IV
  1. The centres of those circles which touch the circle x^(2) + y^(2) - 8...

    Text Solution

    |

  2. IF the tangent at (1,7) to the curve x ^(2) = y-6 touches the circle ...

    Text Solution

    |

  3. Tangent and normal are drawn at P(16,16) on the parabola y^2=16x which...

    Text Solution

    |

  4. The axis of a parabola is along the line y=x and the distance of its v...

    Text Solution

    |

  5. The equations of the common tangents to the parabola y = x^2 and y=-...

    Text Solution

    |

  6. Match the following. Normals are drawn at points P Q and R lying on th...

    Text Solution

    |

  7. Statement-1: The curve y=(-x^(2))/2+x+1 s symmetric with respect to th...

    Text Solution

    |

  8. Consider the circle x^2 + y^2 = 9 and the parabola y^2 = 8x. They inte...

    Text Solution

    |

  9. Consider the circle x^2 + y^2 = 9 and the parabola y^2 = 8x. They inte...

    Text Solution

    |

  10. Consider the circle x^2 + y^2 = 9 and the parabola y^2 = 8x. They inte...

    Text Solution

    |

  11. The tangent and normal at P(t), for all real positive t, to the parabo...

    Text Solution

    |

  12. Let A and B be two distinct points on the parabola y^2 = 4x. If the ax...

    Text Solution

    |

  13. Consider the parabola y^(2) = 8x. Let Delta(1) be the area of the tria...

    Text Solution

    |

  14. Let (x, y) be any point on the parabola y^(2) = 4x. Let P be the point...

    Text Solution

    |

  15. Let L be a normal to the parabola y^(2) = 4x. If L passes through the ...

    Text Solution

    |

  16. Let PQ be a focal chord of the parabola y^2 = 4ax The tangents to the ...

    Text Solution

    |

  17. Let PQ be a focal chord of the parabola y^(2) = 4ax. The tangents to t...

    Text Solution

    |

  18. line L:y=mx+3 meets y–axis at E(0, 3) and the are of the parabola y^(2...

    Text Solution

    |

  19. The common tangents to the circle x^2 + y^2 =2 and the parabola y^2 = ...

    Text Solution

    |

  20. Let a, r, s, t be non-zero real numbers. Let P(at^2, 2at), Q, R(ar^2, ...

    Text Solution

    |