Home
Class 12
MATHS
Prove that the circle x^2 + y^2 -6y + 4 ...

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.

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • Maxima and Minima

    A DAS GUPTA|Exercise EXERCISE|59 Videos

  • Objective Tests

    A DAS GUPTA|Exercise Exercise|36 Videos

Similar Questions

Explore conceptually related problems

Find the area of the quadrilateral formed by common tangents drawn from a point P to the circle x^(2) + y^(2) = 8 and the parabola y^(2) =16x , chord of contact of tangents to the circle and chord of contact of tangents to the parabolas.

If the line x+y=1 touches the parabola y^(2)-y+x=0 ,then the coordinates of the point of contact are:

Find the coordinates of the points at which the circles x^2+y^2-4x-2y=4 and x^2+y^2-12x-8y=12 touch each other. Find the coordinates of the point of contact and equation of the common tangent at the point of contact.

If the circle x^(2)+y^(2)+2ax=0, a in R touches the parabola y^(2)=4x , them

Two common tangents to the circle x^(2) + y^(2) = (a^(2))/(2) and the parabola y^(2) = 4ax are

Show that the circles x^(2)+y^(2)-10x+4y-20=0 and x^(2)+y^(2)+14x-6y+22=0 touch each other.Find the coordinates of the point of contact and the equation of the common tangent at the point of contact.

Equation of a common tangent to the circle x^(2)+y^(2)-6x=0 and the parabola y^(2)=4x is

find the coordinates of the points at which the circle x^(2)+y^(2)-4x-2y=4 and x^(2)+y^(2)-12x-8y=12 touch each other.Find the equation of the common tangent at the point of contact.

Prove that the circle x^(2)+y^(2)+2x+2y+1=0 and circle x^(2)+y^(2)-4x-6y-3=0 touch each other.

A DAS GUPTA-Miscellaneous Exercises-Exercise
  1. The equation of two equal sides AB and AC of an isosceies triangle ABC...

    Text Solution

    |

  2. Find the equation of the largest circle with centre (1, 0) that can be...

    Text Solution

    |

  3. Prove that the circle x^2 + y^2 -6y + 4 = 0 and the parabola y^(2) = x...

    Text Solution

    |

  4. Find the equation of the ellipse whose foci are the points (1, 2) and ...

    Text Solution

    |

  5. Let ABC and PQR be any two triangles in the same plane. Assume that th...

    Text Solution

    |

  6. An unbiased dice, with faces numbered 1, 2, 3, 4, 5, 6, is thrown n ti...

    Text Solution

    |

  7. Find the smallest positive values of xa n dy satisfying x-y=pi/4a n dc...

    Text Solution

    |

  8. log(3/4)log8(x^2+7)+log(1/2)log(1/4)(x^2+7)^(-1)=-2.

    Text Solution

    |

  9. Total number of solutions of the equation x² -4-[x]=0 are (where (.) d...

    Text Solution

    |

  10. Let a, b be the roots of the equation x^2 - kx + k = 0, k in R. If a^2...

    Text Solution

    |

  11. Two parabola have the focus (3, 2). Their directrices are the x-axis a...

    Text Solution

    |

  12. Let alpha in R. prove that a function f: R-R is differentiable at...

    Text Solution

    |

  13. Find the lim(x to 0) frac{sqrt(x+2) -sqrt2}{root(3)(1-x) - sqrt(1+x)}.

    Text Solution

    |

  14. Two parabolas y(2) = 4a(x – 1l(1)) and x(2) = 4a(y – l(2)) always touc...

    Text Solution

    |

  15. Let 2x^2 +y^2-3xy = 0 be the equation of a pair of tangents drawn from...

    Text Solution

    |

  16. Let f(x),xgeq0, be a non-negative continuous function, and let f(x)...

    Text Solution

    |

  17. Let b!=0 and for j=0,1,2,....,n. Let S(j) be the area of the region bo...

    Text Solution

    |

  18. Let P be a point on the ellipse x^2/a^2+y^2/b^2=1 , 0 < b < a and le...

    Text Solution

    |

  19. A hemi-spherical tank of radius 2 m is initially full of water and ...

    Text Solution

    |

  20. I(n) is the area of n sided refular polygon inscribed in a circle unit...

    Text Solution

    |