Home
Class 12
MATHS
Prove that the parabola y^(2) = 16x and ...

Prove that the parabola `y^(2) = 16x` and the circle `x^(2) + y^(2) - 40x - 16y - 48 = 0` meet at the point P(36, 24) and one other point Q. Prove that PQ is a diameter of the circle. Find Q.

Text Solution

Verified by Experts

The correct Answer is:
`(4,-8)`
Promotional Banner

Topper's Solved these Questions

  • PARABOLA

    MOTION|Exercise EXERCISE - IV|33 Videos

  • PARABOLA

    MOTION|Exercise EXERCISE - II|17 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

Two points on the circle x^(2) + y^(2) - 12x - 16y + 75 = 0 , one nearest to the origin and the other farthest from are

A circle C touches the line x = 2y at the point (2, 1) and intersects the circle C_1 : x^2 + y^2 + 2y -5 = 0 at two points P and Q such that PQ is a diameter of C^1 . Then the diameter of C is :

Let P be the point on the parabola y^(2) = 4x which is at the shortest distance from the centre S of the circle x^(2) + y^(2) - 4x - 16y + 64 = 0 . Let Q be the point on the circle dividing the lie segment SP internally. Then

The tangent to the parabola y=x^(2)-2x+8 at P(2, 8) touches the circle x^(2)+y^(2)+18x+14y+lambda=0 at Q. The coordinates of point Q are

If line y = 4x meets circle x^(2) + y^(2) - 17 x = 0 in points A and B , then equation of circle of which AB is a diameter is

Prove that the circle x^2 + y^2 -6y + 4 = 0 and the parabola y^(2) = x touch. Find the common tangent at the point of contact.

The line x=2y intersects the ellipse (x^(2))/4+y^(2)=1 at the points P and Q . The equation of the circle with PQ as diameter is

If line y= 2x meets circle x^(2) + y^(2) - 4x = 0 in point A and B , then equation of circle of which AB is diameter is

If the normal to the parabola y^(2)=12x at the point P(3,6) meets the parabola again at the point Q,then equation of the circle having PQ as a diameter is

MOTION-PARABOLA-EXERCISE - III
  1. From vertex O ofthe parabola y^2=4ax perpendicular is drawn at a tange...

    Text Solution

    |

  2. Let P be a point on the parabola y^(2) - 2y - 4x+5=0, such that the ta...

    Text Solution

    |

  3. Two tangents to the parabola y^(2) = 8x meet the tangent at its vertex...

    Text Solution

    |

  4. Show that the normals at the points (4a, 4a) & at the upper end of t...

    Text Solution

    |

  5. In the parabola y^(2) = 4ax, the tangent at the point P, whose absciss...

    Text Solution

    |

  6. Prove that the locus of the middle point of portion of a normal to y^(...

    Text Solution

    |

  7. Three normals to y^2=4x pass through the point (15, 12). Show that one...

    Text Solution

    |

  8. Normals are drawn from a point P with slopes m1,m2 and m3 are drawn fr...

    Text Solution

    |

  9. Prove that, the normal to y^(2) = 12x at (3,6) meets the parabola agai...

    Text Solution

    |

  10. P & Q are the points of contact of the tangents drawn from the point T...

    Text Solution

    |

  11. A variable chord PQ of the parabola y^(2) = 4x is drawn parallel to th...

    Text Solution

    |

  12. Show that the normals at two suitable distinct real points on the para...

    Text Solution

    |

  13. Let S is the focus of the parabola y^(2) = 4ax and X the foot of the d...

    Text Solution

    |

  14. Prove that the parabola y^(2) = 16x and the circle x^(2) + y^(2) - 40x...

    Text Solution

    |

  15. .Find the equation ofthe circle which passes through the focus ofthe p...

    Text Solution

    |

  16. A fixed parabola y^(2) = 4ax touches a variable parabola. Find the equ...

    Text Solution

    |

  17. Show that an infinite number of triangles can be inscribed in either o...

    Text Solution

    |

  18. From the point P(h, k) three normals are drawn to the parabola x^(2) =...

    Text Solution

    |

  19. From the point P(h, k) three normals are drawn to the parabola x^(2) =...

    Text Solution

    |

  20. From the point P(h, k) three normals are drawn to the parabola x^(2) =...

    Text Solution

    |