Home
Class 11
MATHS
Show that the circles x^2+y^2-10 x+4y-20...

Show that the circles `x^2+y^2-10 x+4y-20=0` and `x^2+y^2+14 x-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.

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    CENGAGE ENGLISH|Exercise All Questions|886 Videos
  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE ENGLISH|Exercise Multiple correct answers type|11 Videos

Similar Questions

Explore conceptually related problems

Show that the circles x^(2) +y^(2) - 2x - 4y - 20 = 0 and x^(2) + y^(2) + 6x +2y- 90=0 touch each other . Find the coordinates of the point of contact and the equation of the common tangent .

Show that the circle x^(2) +y^(2) - 6x -2y + 1 = 0, x^(2) + y^(2) + 2x - 8y + 13 = 0 touch each other. Find the point of contact and the equation of common tangent at their point of contact.

Show that the circles x^2 + y^2 - 2x-6y-12=0 and x^2 + y^2 + 6x+4y-6=0 cut each other orthogonally.

Circles x^(2) + y^(2) - 2x = 0 and x^(2) + y^(2) + 6x - 6y + 2 = 0 touch each other extermally. Then point of contact is

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.

Show that the circle x^(2)+ y^(2) - 4x + 4y + 4 = 0 touches the co-ordinate axes. If the points of contact are A and B, find the equation of the circle which passes through A, B and the origin,

Prove that the curve y^2=4x and x^2 +y^2 - 6x +1=0 touches each other at thepoint (1, 2), find the equation of the common tangents.

The point at which the circles x^(2)+y^(2)-4x-4y+7=0 and x^(2)+y^(2)-12x-10y+45=0 touch each other is

Show that the circles x^(2) + y^(2) + 2x = 0 and x^(2)+ y^(2) - 6 x -6 y + 2 = 0 touch externally at the point (1/5,3/5)

Show that the straight line x + y=1 touches the hyperbola 2x ^(2) - 3y ^(2)= 6. Also find the coordinates of the point of contact.

CENGAGE ENGLISH-CONIC SECTIONS-All Questions
  1. Find the equations to the common tangents of the circles x^2+y^2-2x-6y...

    Text Solution

    |

  2. Equation of the smaller circle that touches the circle x^2+y^2=1 and p...

    Text Solution

    |

  3. Show that the circles x^2+y^2-10 x+4y-20=0 and x^2+y^2+14 x-6y+22=0 to...

    Text Solution

    |

  4. If the radical axis of the circles x^2+y^2+2gx+2fy+c=0 and 2x^2+2y^2+3...

    Text Solution

    |

  5. The equation of three circles are given x^2+y^2=1,x^2+y^2-8x+15=0,x^2+...

    Text Solution

    |

  6. If the circles x^2+y^2+2a^(prime)x+2b^(prime)y+c^(prime)=0 and 2x^2+2...

    Text Solution

    |

  7. A circle passes through the origin and has its center on y=x If it cut...

    Text Solution

    |

  8. Prove that the equation of any tangent to the circle x^2+y^2-2x+4y-4=0...

    Text Solution

    |

  9. The tangent to the circle x^2+y^2=5 at (1,-2) also touches the circle ...

    Text Solution

    |

  10. If S(1)=alpha^(2)+beta^(2)-a^(2), then angle between the tangents from...

    Text Solution

    |

  11. If a >2b >0, then find the positive value of m for which y=m x-bsqrt(1...

    Text Solution

    |

  12. Find the angle between the two tangents from the origin to the circle ...

    Text Solution

    |

  13. Two circles C1 and C2 intersect at two distinct points PandQ in a line...

    Text Solution

    |

  14. Find the equation of the tangent at the endpoints of the diameter of ...

    Text Solution

    |

  15. Find the equations of the tangents to the circle x^2+y^2-6x+4y=12 whic...

    Text Solution

    |

  16. If from any point P on the circle x^2+y^2+2gx+2fy+c=0, tangents are dr...

    Text Solution

    |

  17. The lengths of the tangents from P(1,-1) and Q(3,3) to a circle are sq...

    Text Solution

    |

  18. Which of the following is a point on the common chord of the circle x^...

    Text Solution

    |

  19. If the circles x^2+y^2+2a x+c y+a=0 and x^2+y^2-3a x+d y-1=0 intersec...

    Text Solution

    |

  20. Find the angle at which the circles x^2+y^2+x+y=0 and x^2+y^2+x-y=0 in...

    Text Solution

    |