Home
Class 12
MATHS
The tangents to x^2+y^2=a^2 having incli...

The tangents to `x^2+y^2=a^2` having inclinations `alpha` and `beta` intersect at `P`. If `cotalpha+cotbeta=0` , then find the locus of `P`

A

`x+y=0`

B

`x-y=0`

C

`xy=0`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • CIRCLES

    OBJECTIVE RD SHARMA|Exercise Chapter Test|55 Videos

  • CIRCLES

    OBJECTIVE RD SHARMA|Exercise Section II - Assertion Reason Type|12 Videos

  • CARTESIAN PRODUCT OF SETS AND RELATIONS

    OBJECTIVE RD SHARMA|Exercise Chapter Test|31 Videos

  • COMPLEX NUMBERS

    OBJECTIVE RD SHARMA|Exercise Chapter Test|59 Videos

Similar Questions

Explore conceptually related problems

The tangents to x^(2)+y^(2)=a^(2) having inclinations alpha and beta intersect at P. If cot alpha+cot beta=0, then find the locus of P.

The tangents to x^(2)+y^(2)=r^(2) having inclinations theta_(1),theta_(2) intersect at P .If tan theta_(1)-tan theta_(2)=1 locus of P is

If the eccentric angles of two points P and Q on the ellipse x^2/a^2+y^2/b^2 are alpha,beta such that alpha +beta=pi/2 , then the locus of the point of intersection of the normals at P and Q is

Prove that the locus of a point,tangents from where to hyperbola x^(2)-y^(2)=a^(2) inclined at an angle alpha& beta with x-axis such that tan alpha tan beta=2 is also a hyperbola.Find the eccentricity of this hyperbola.

Let P be a point on the hyperbola x^(2)-y^(2)=a^(2), where a is a parameter,such that P is nearest to the line y=2x. Find the locus of P.

Find the condition that the chord of contact of tangents from the point (alpha, beta) to the circle x^2 + y^2 = a^2 should subtend a right angle at the centre. Hence find the locus of (alpha, beta) .

Two tangents drawn on parabola y^(2)=4ax are making angle alpha_ _(1)and alpha_(2), with y -axis and if alpha_(1)+alpha_(2)=2 beta then locus of the point of intersection of these tangent is

If the tangent from a point p to the circle x^(2)+y^(2)=1 is perpendicular to the tangent from p to the circle x^(2)+y^(2)=3, then the locus of p is

Two tangents to the parabola y^(2) = 8x meet the tangent at its vertex in the points P & Q. If PQ = 4 units, prove that the locus of the point of the intersection of the two tangents is y^(2) = 8 (x + 2) .

OBJECTIVE RD SHARMA-CIRCLES-Exercise
  1. Find the angle which the common chord of x^2+y^2-4x=0 and x^2+y^2=16 s...

    Text Solution

    |

  2. Show that the equation of the circle passing through (1, 1) and the ...

    Text Solution

    |

  3. The tangents to x^2+y^2=a^2 having inclinations alpha and beta interse...

    Text Solution

    |

  4. Equation of a circle with centre(4,3) touching the circle x^2+y^2=1

    Text Solution

    |

  5. Find the number of common tangents that can be drawn to the circles...

    Text Solution

    |

  6. If 3x+y=0 is a tangent to a circle whose center is (2,-1) , then find ...

    Text Solution

    |

  7. Find the condition if the circle whose equations are x^2+y^2+c^2=2a x ...

    Text Solution

    |

  8. The distance between the chords of contact of tangents to the circle x...

    Text Solution

    |

  9. The condition that the chord xcosalpha+ysinalpha=p=0 of x^2+y^2-a^2=0 ...

    Text Solution

    |

  10. The locus of the centres of the circles which touch x^2+y^2=a^2 and x^...

    Text Solution

    |

  11. Let P be a point on the circle x^2+y^2=9,Q a point on the line 7x+y+3=...

    Text Solution

    |

  12. Two lines through (2, 3) from which the circle x^2+y^2 =25 intercepts ...

    Text Solution

    |

  13. A line meets the coordinate axes at A and B . A circle is circumscribe...

    Text Solution

    |

  14. Find the co-ordinate of the point on the circle x^2+y^2-12x-4y +30=0, ...

    Text Solution

    |

  15. If the angle of intersection of the circle x^2+y^2+x+y=0 and x^2+y^2+x...

    Text Solution

    |

  16. Find the equation of the circle whose radius is 5a n d which touches t...

    Text Solution

    |

  17. A B is a diameter of a circle and C is any point on the circle. ...

    Text Solution

    |

  18. The locus of the mid point of a chord of the circle x^2+y^2=4 which su...

    Text Solution

    |

  19. The point of which the line 9x + y - 28 = 0 is the chord of contact of...

    Text Solution

    |

  20. If the tangents are drawn to the circle x^2+y^2=12 at the point where ...

    Text Solution

    |