Home
Class 11
MATHS
If the chords of contact of tangents fro...

If the chords of contact of tangents from two poinst `(x_1, y_1)` and `(x_2, y_2)` to the ellipse `(x^2)/(a^2)+(y^2)/(b^2)=1` are at right angles, then find the value of `(x_1x_2)/(y_1y_2)dot`

Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    CENGAGE PUBLICATION|Exercise All Questions|877 Videos

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE PUBLICATION|Exercise Multiple correct answers type|11 Videos

Similar Questions

Explore conceptually related problems

If the chords of contact of tangents from two points (-4,2) and (2,1) to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 are at right angle, then find then find the eccentricity of the hyperbola.

If the chord of contact of tangents from a point (x_1,y_1) to the circle x^2+y^2=a^2 touches the circle (x-a)^2+y^2=a^2 , then the locus of (x_1,y_1) is :

Find the maximum area of the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 which touches the line y=3x+2.

Find the locus of middle points of chords of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 which subtend right angle at its center.

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

Two tangents are drawn from a point on hyperbola x^(2)-y^(2)=5 to the ellipse (x^(2))/(9)+(y^(2))/(4)=1 . If they make angle alpha and beta with x-axis, then

If the chord of contact of tangents from a point on the circle x^(2) + y^(2) = a^(2) to the circle x^(2)+ y^(2)= b^(2) touches the circle x^(2) + y^(2) = c^(2) , then a, b, c are in-

Tangents are drawn from any point on the circle x^(2)+y^(2) = 41 to the ellipse (x^(2))/(25)+(y^(2))/(16) =1 then the angle between the two tangents is

If the foci of the ellipse (x^2)/(16)+(y^2)/(b^2)=1 and the hyperbola (x^2)/(144)-(y^2)/(81)=1/(25) coincide, then find the value of b^2

If x/a+y/b=sqrt2 touches the ellipses x^2/a^2+y^2/b^2=1 , then find the ecentricity angle theta of point of contact.

CENGAGE PUBLICATION-CONIC SECTIONS-All Questions
  1. Find the locus of the middle points of all chords of (x^2)/4+(y^2)/...

    Text Solution

    |

  2. Tangents P Qa n dP R are drawn at the extremities of the chord of th...

    Text Solution

    |

  3. If the chords of contact of tangents from two poinst (x1, y1) and ...

    Text Solution

    |

  4. From the point A(4,3), tangent are drawn to the ellipse (x^2)/(16)...

    Text Solution

    |

  5. An ellipse is drawn with major and minor axis of length 10 and 8 resp...

    Text Solution

    |

  6. Find the foci of the ellipse 25(x+1)^2+9(y+2)^2=225.

    Text Solution

    |

  7. Find the equation of an ellipse whose axes are the x-and y-axis and...

    Text Solution

    |

  8. If P(alpha,beta) is a point on the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1...

    Text Solution

    |

  9. An arc of a bridge is semi-elliptical with the major axis horizonta...

    Text Solution

    |

  10. An ellipse has O B as the semi-minor axis, F and F ' as its foci, ...

    Text Solution

    |

  11. P is a variable on the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 with A A ' ...

    Text Solution

    |

  12. Prove that the curve represented by x=3(cost+sint),y=4(cost-sint),t in...

    Text Solution

    |

  13. Find the center, foci, the length of the axes, and the eccentricity...

    Text Solution

    |

  14. If C is the center and A ,B are two points on the conic 4x^2+9y^...

    Text Solution

    |

  15. Find the equation of a chord of the ellipse (x^2)/(25)+(y^2)/(16)=1 jo...

    Text Solution

    |

  16. Prove that the chords of contact of pairs of perpendicular tangents to...

    Text Solution

    |

  17. Tangent are drawn from the point (3, 2) to the ellipse x^2+4y^2=9 ....

    Text Solution

    |

  18. Find the locus of the point of intersection of tangents to the elli...

    Text Solution

    |

  19. Tangents are drawn from the points on the line x−y−5=0 to x^2+4y^2=4, ...

    Text Solution

    |

  20. If from a point P , tangents PQ and PR are drawn to the ellipse (x^2...

    Text Solution

    |