Home
Class 11
MATHS
Find the intervals of the values of 'a' ...

Find the intervals of the values of 'a' for which the line y + x = 0 bisects two chords drawn from a point `((1+sqrt2a)/2,(1-sqrt2a)/2)` to the circle
`2x^2+2y^2-(1+sqrt2a)x-(1-sqrt2a)y=0`

Text Solution

Verified by Experts

`a in (- infty,-2)cup(2,infty)`
Promotional Banner

Topper's Solved these Questions

  • CARTESIAN COORDINATES AND STRAIGHT LINE

    PATHFINDER|Exercise QUESTION BANK|249 Videos
  • COMPLEX NUMBER

    PATHFINDER|Exercise QUESTION BANK|224 Videos

Similar Questions

Explore conceptually related problems

Find the lengths of the tangents drawn from the point. (x_(1),y_(1)) to the circle x^(2)+y^(2)+2x=0

Find the lengths of the tangents drawn from the point. (-1,1) to the circle x^(2)+y^(2)-2x+4y+1=0

Find the equation of the plane containing the lines 2x-y+z-3=0,3x+y+z=5 and a t a distance of 1/sqrt6 from the point (2,1,-1).

Find the equation of the circle which is concentric with the circle 2x^(2) + 2y^(2) + 5x - 7y - 1 = 0 and whose radius is (1)/(4)sqrt(26) unit.

Find the equation of the normal to the circle x^2+y^2=9 at the point (1/(sqrt(2)),1/(sqrt(2))) .

Find the obtuse angle between the lines x-y+2=0 and (2-sqrt(3))x-y+1=0 .

The coordinates of a point on the line x + y + 1 = 0 which is at a distance sqrt(2) units from the line 3x + 4y - 2 = 0 are

Prove that the product of the lengths of the perpendiculars drawn from the points (sqrt(a^2-b^2),0) and (-sqrt(a^2-b^2),0) to the line x/a costheta + y/b sintheta=1 is b^2 .

If x= (sqrt2+1)/(sqrt2-1) and x-y= 4sqrt2 then find the value of x^4+y^4 .

The length of the chord of the parabola y^2=x which is bisected at the point (2, 1) is 2sqrt(3) (b) 4sqrt(3) (c) 3sqrt(2) (d) 2sqrt(5)

PATHFINDER-CIRCLE-QUESTION BANK
  1. The equation of the circle which touches the axis of y at a distance +...

    Text Solution

    |

  2. The circle x^2+y^2-4x-4y+4=0 is inscribed in a triangle which has two ...

    Text Solution

    |

  3. Find the intervals of the values of 'a' for which the line y + x = 0 b...

    Text Solution

    |

  4. If the two lines a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0 cut the co-...

    Text Solution

    |

  5. If y = mx is the equation of a chord of the circle x^2+y^2-2ax=0 with ...

    Text Solution

    |

  6. Find the locus of the mid point of the chord of the circle x^2+y^2=a^2...

    Text Solution

    |

  7. Tangents are drawn to the circle x^2+y^2=4 from P(3,4) to touch it at ...

    Text Solution

    |

  8. Show that the common tangents to the circles x^2+y^2-6x=0 and x^2+y^2+...

    Text Solution

    |

  9. Two straight lines rotate about two fixed points. If they start from t...

    Text Solution

    |

  10. If two curves, whose equations are ax^2+2hxy+by^2+2gx+2fy+c=0 and a'x^...

    Text Solution

    |

  11. Find the equation of the circle of minimum radius which contains the t...

    Text Solution

    |

  12. The number of common tangents to the circles x^2+y^2-4x-6y-12=0 and x^...

    Text Solution

    |

  13. A circle S passes through the point (0, 1) and is orthogonal to the ci...

    Text Solution

    |

  14. Let C be the circle with centre at (1, 1) and radius = 1. If T is the ...

    Text Solution

    |

  15. The circle passing through (1, - 2) and touching the axis of x at (3, ...

    Text Solution

    |

  16. A point P lines on the circle x^2+y^2=169. If Q = (5, 12) and R= (-12,...

    Text Solution

    |

  17. A circle passing through (0, 0), (2, 6), (6, 2) cuts the x-axis at the...

    Text Solution

    |

  18. A point moves so that the sum of squares of its distances from the poi...

    Text Solution

    |

  19. If one end of a diameter of the circle x^2+y^2-4x-6y+11=0 is (3, 4) th...

    Text Solution

    |

  20. The equation of the circle passing through the point (1, 1) and the po...

    Text Solution

    |