Home
Class 11
MATHS
If x/a+y/b=sqrt2 touches the ellipses x^...

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.

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 hyperbola (x^2)/(b^2)-(y^2)/(a^2)=1 passes through the focus of ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 , then find the eccentricity of hyperbola.

If omega is one of the angles between the normals to the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 (b>a) at the point whose eccentric angles are theta and pi/2+theta , then prove that (2cotomega)/(sin2theta)=(e^2)/(sqrt(1-e^2))

Show that the straight line (x)/(a)+(y)/(b)=2 touches the curve ((x)/(a))^(3)+((y)/(b))^(3)=2 , find the coordinates of the point of contact.

If eccentric angle of a point lying in the first quadrant on the ellipse x^2/a^2 + y^2/b^2 = 1 be theta and the line joining the centre to that point makes an angle phi with the x-axis, then theta - phi will be maximum when theta is equal to

If the coordinates of a point lies on the ellipse 9x^2+16y^2=144 be (2,(3sqrt3)/2) ,find the eccentric angle of that point.

If the line l x+m y+n=0 cuts the ellipse ((x^2)/(a^2))+((y^2)/(b^2))=1 at points whose eccentric angles differ by pi/2, then find the value of (a^2l^2+b^2m^2)/(n^2) .

If the coordinates of a point lies on the ellipse 9x^(2) + 16y^(2) = 144 be (2 , (3sqrt(3))/(2)) , find the eccentric angle of that point .

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.

A tangent is drawn to the ellipse to cut the ellipse x^2/a^2+y^2/b^2=1 and to cut the ellipse x^2/c^2+y^2/d^2=1 at the points P and Q. If the tangents are at right angles, then the value of (a^2/c^2)+(b^2/d^2) is

The coordinates of the point on the ellipse 9x^(2) + 16y^(2) = 144 are (2,(3sqrt(3))/(2)) , find the eccentric angle of the point .

CENGAGE PUBLICATION-CONIC SECTIONS-All Questions
  1. Find the eccentricity, one of the foci, the directrix, and the leng...

    Text Solution

    |

  2. An ellipse passes through the point (4,-1) and touches the line x+4...

    Text Solution

    |

  3. If x/a+y/b=sqrt2 touches the ellipses x^2/a^2+y^2/b^2=1, then find the...

    Text Solution

    |

  4. Find the points on the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 such that the...

    Text Solution

    |

  5. An ellipse slides between two perpendicular straight lines. Then id...

    Text Solution

    |

  6. Find the locus of the foot of the perpendicular drawn from the cent...

    Text Solution

    |

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

    Text Solution

    |

  8. Tangent is drawn to ellipse (x^2)/(27)+y^2=1 at (3sqrt(3)costheta,sint...

    Text Solution

    |

  9. Consider an ellipse (x^2)/4+y^2=alpha(alpha is parameter >0) and a ...

    Text Solution

    |

  10. Find the angle between the pair of tangents from the point (1,2) to...

    Text Solution

    |

  11. If the chord joining points P(alpha) and Q(beta) on the ellipse ((x^...

    Text Solution

    |

  12. If alpha and beta are the eccentric angles of the extremities of a f...

    Text Solution

    |

  13. If the area of the ellipse ((x^2)/(a^2))+((y^2)/(b^2))=1 is 4pi , then...

    Text Solution

    |

  14. The center of an ellipse is C and P N is any ordinate. Point A ,A ' ar...

    Text Solution

    |

  15. The ratio of the area of triangle inscribed in ellipse x^2/a^2+y^2/b^...

    Text Solution

    |

  16. If PSQ is a focal chord of the ellipse 16x^2+25y^2=400 such that SP=8,...

    Text Solution

    |

  17. A O B is the positive quadrant of the ellipse (x^2)/(a^2)+(y^2)/(b^2)=...

    Text Solution

    |

  18. If Sa n dS ' are two foci of ellipse 16 x^2+25 y^2=400 and P S Q is ...

    Text Solution

    |

  19. Find the equations of the tangents drawn from the point (2, 3) to t...

    Text Solution

    |

  20. Prove that area common to ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 and its au...

    Text Solution

    |