Home
Class 12
MATHS
Tangents are drawn to the circle x^2+y^2...

Tangents are drawn to the circle `x^2+y^2=12` at the points where it is met by the circle `x^2+y^2-5x+3y-2=0` . Find the point of intersection of these tangents.

Text Solution

Verified by Experts

The equation of the common chord AB of the given circles is
`(x^(2) +y^(2) -12) - (x^(2) + y^(2) -5x + 3y -2)=0`
`rArr 5x - 3y - 10=0" " …(i)`
Let P(h, k) be the point of intersection of the tangents drawn to the circle `x^(2) + y^(2) = 12`. Then AB is the chord of contact of tangents drawn from P.
`therefore` The equation of AB is `xh + yk = 12 " "...(ii)`
Comparing (i) and (ii), we get
`(h)/(5)=(k)/(-3) = (-12)/(-10)`
`therefore` Required point is `(6, (-18)/(5))`.
Promotional Banner

Topper's Solved these Questions

  • CONIC SECTIONS

    AAKASH INSTITUTE ENGLISH|Exercise Try ypurself|42 Videos

  • CONIC SECTIONS

    AAKASH INSTITUTE ENGLISH|Exercise Assignment (SECTION - A)|55 Videos

  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    AAKASH INSTITUTE ENGLISH|Exercise section-J (Aakash Challengers Qestions)|13 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    AAKASH INSTITUTE ENGLISH|Exercise section - J|6 Videos

Similar Questions

Explore conceptually related problems

If the tangents are drawn to the circle x^2+y^2=12 at the point where it meets the circle x^2+y^2-5x+3y-2=0, then find the point of intersection of these tangents.

Tangents are drawn to the circle x^2+y^2=9 at the points where it is met by the circle x^2+y^2+3x+4y+2=0 . Find the point of intersection of these tangents.

Tangents are drawn to the circle x^(2)+y^(2)=16 at the points where it intersects the circle x^(2)+y^(2)-6x-8y-8=0 , then the point of intersection of these tangents is

Tangents are drawn to the circle x^(2)+y^(2)=9 at the points where it is cut by the line 4x+3y-9=0 then the point of intersection of tangents is

Tangents are drawn to the parabola y^2=4a x at the point where the line l x+m y+n=0 meets this parabola. Find the point of intersection of these tangents.

Tangents are drawn to the parabola y^2=4a x at the point where the line l x+m y+n=0 meets this parabola. Find the point of intersection of these tangents.

Tangent are drawn to the circle x^2+y^2=1 at the points where it is met by the circles x^2+y^2-(lambda+6)x+(8-2lambda)y-3=0,lambda being the variable. The locus of the point of intersection of these tangents is 2x-y+10=0 (b) 2x+y-10=0 x-2y+10=0 (d) 2x+y-10=0

Find the point of intersection of the circle x^2+y^2-3x-4y+2=0 with the x-axis.

The tangent to the circle x^2+y^2=5 at (1,-2) also touches the circle x^2+y^2-8x+6y+20=0 . Find the coordinats of the corresponding point of contact.

From an arbitrary point P on the circle x^2+y^2=9 , tangents are drawn to the circle x^2+y^2=1 , which meet x^2+y^2=9 at A and B . The locus of the point of intersection of tangents at A and B to the circle x^2+y^2=9 is (a) x^2+y^2=((27)/7)^2 (b) x^2-y^2((27)/7)^2 y^2-x^2=((27)/7)^2 (d) none of these

AAKASH INSTITUTE ENGLISH-CONIC SECTIONS-SECTION - J ( Aakash Challengers Questions )
  1. Tangents are drawn to the circle x^2+y^2=12 at the points where it is ...

    Text Solution

    |

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

    Text Solution

    |

  3. The area of the triangle formed by the tangent at (3, 4) to the circle...

    Text Solution

    |

  4. If P(1), P(2), P(3) are the perimeters of the three circles, S(1) :...

    Text Solution

    |

  5. If (1, a), (b, 2) are conjugate points with repect to the circle x^(2)...

    Text Solution

    |

  6. Area of the equilateral triangle inscribed in the circle x^(2) + y^(2)...

    Text Solution

    |

  7. A solid sphere of radius R/2 is cut out of a solid sphere of radius R ...

    Text Solution

    |

  8. The range of parameter ' a ' for which the variable line y=2x+a lies b...

    Text Solution

    |

  9. A planet of mass m moves along an ellipse around the sun (mass M) so t...

    Text Solution

    |

  10. There are exactly two points on the ellipse x^2/a^2+y^2/b^2=1,whose di...

    Text Solution

    |

  11. The line2px+ysqrt(1-p^(2))=1(abs(p)lt1) for different values of p, tou...

    Text Solution

    |

  12. A point P moves such that the sum of the slopes of the normals drawn f...

    Text Solution

    |

  13. A rectangular hyperbola whose centre is C is cut by any circle of radi...

    Text Solution

    |

  14. Let P be a point on the hyperbola x^2-y^2=a^2, where a is a parameter,...

    Text Solution

    |

  15. Tangents are drawn from the points on a tangent of the hyperbola x^2-y...

    Text Solution

    |

  16. A tangent to the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 cuts the ellipse ...

    Text Solution

    |

  17. Let F(x) = (1+b^(2))x^(2) + 2bx + 1. The minimum value of F(x) is the ...

    Text Solution

    |