Home
Class 12
MATHS
The common tangent of the parabola y^(2)...

The common tangent of the parabola `y^(2) = 8ax` and the circle `x^(2) + y^(2) = 2a^(2)` is

Text Solution

Verified by Experts

Any tangent to parabola is
`y=mx+(2a)/m`
Solving with the circle
`x^(2)+(mx+(2a)/m)^(2)=2a^(2)`
`!x^(2)(1+m^(2))+4ax+(4a^(2))/(m^(2))-2a^(2)=0`
`B^(2)-4AC=0` gives `m=pm1`
Tangent
`y=pmxpm2a`
Promotional Banner

Topper's Solved these Questions

  • PARABOLA

    MOTION|Exercise EXERCISE - I|28 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

The equation of the common tangent to the parabola y^(2) = 8x and the hyperbola 3x^(2) – y^(2) = 3 is

If m is the slope of a common tangent of the parabola y^(2)=16x and the circle x^(2)+y^(2)=8 , then m^(2) is equal to

The common tangent to the parabolas y^(2)=8x and x^(2)=-4y is

Equation of a common tangent to the parabola y^(2)=8x and the circle x^(2)+y^(2)=2 can be

Show that the common tangents to the parabola y^(2)=4x and the circle x^(2)+y^(2)+2x=0 form an equilateral triangle.

The equation of one of the common tangent to the parabola y^(2) = 8x and x^(2) + y^(2) -12x + 4 = 0 is

The common tangent of the parabolas y^(2)=4x" and "x^(2)=-8y, is

If the common tangents to the parabola y^(2)=4ax and circle x^(2)+y^(2)=c^(2) makes an angle theta with x axis then tan^(2)theta

Length of the common chord of the parabola y^(2)=8x and the circle x^(2)+y^(2)-2x-4y=0 is :

The slopes of the common tangents to the parabola y^(2)=24x and the hyperbola 5x^(2)-y^(2)=5 are

MOTION-PARABOLA-EXERCISE - IV
  1. The common tangent of the parabola y^(2) = 8ax and the circle x^(2) + ...

    Text Solution

    |

  2. The locus of the vertex of the family of parabolas y=(a^3x^2)/3+(a^(2x...

    Text Solution

    |

  3. The equation of a tangent to the parabola y^2=""8x""i s""y""=""x""+...

    Text Solution

    |

  4. A parabola has the origin as its focus and the line x""=""2 as the ...

    Text Solution

    |

  5. If two tangents drawn from a point P to the parabola y2 = 4x are at ri...

    Text Solution

    |

  6. Given : A circle, 2x^2+""2y^2=""5 and a parabola, y^2=""4sqrt(5)""x . ...

    Text Solution

    |

  7. The equation to the line touching both the parabolas y^2 =4x and x^2=...

    Text Solution

    |

  8. Let O be the vertex and Q be any point on the parabola,x^2=""8y . I...

    Text Solution

    |

  9. Let , P be the point on the parabola y^(2) = 8x which is at a min...

    Text Solution

    |

  10. The centres of those circles which touch the circle x^(2) + y^(2) - 8...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |