Home
Class 12
MATHS
The condition that y=m x+c is a tangent ...

The condition that `y=m x+c` is a tangent to the ellipse `(x^(2))/(a^(2))+(y^(2))/(b^(2))`=1 is

A

`c^(2)=a^(2) m^(2)+b^(2)`

B

`a^(2)=c^(2) m^(2)+b^(2)`

C

`b^(2)-a^(2) m^(2)+c^(2)`

D

`b^(2)=a^(2) m^(2)-c^(2)`

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • ELLIPSE

    HIMALAYA PUBLICATION|Exercise QUESTION BANK|172 Videos

  • INDEFINITE INTEGRAL

    HIMALAYA PUBLICATION|Exercise QUESTION BANK|404 Videos

Similar Questions

Explore conceptually related problems

Sum of focal distances of an ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 is :

The product of the perpendiculars from the foci on any tangent to the ellipse (x^(2))/(a^(2)) + (y^(2))/(b^(2)) = 1 is

If y=m x+c is a tangent to (x^(2))/(a^(2))+(y^(2))/(b^(2)) = 1 then b^(2) =

The locus of the middle point of the portion of a tangent to the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 included between the axes is the curve

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

If sqrt(3) b x+a y=2 a b is a tangent to the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 then the eccentric angle of the point is

The line L x+m y+n=0 is a normal to the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 , if

If e is the eccentricity of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 , (altb) then

The line x+y=a will be a tangent to the ellipse (x^(2))/(9)+(y^(2))/(16)=1 , if a=

Find the area of the ellipse (x^(2))/(a^(2))+ (y^(2))/(b^(2))=1 by the method of integration.

HIMALAYA PUBLICATION-HYPERBOLA-QUESTION BANK
  1. The distance between the foci of a hyperbola is 16 and its eccentricit...

    Text Solution

    |

  2. The equation of the hyperbola with eccentricity 3/2 and foci at (pm2,0...

    Text Solution

    |

  3. The condition that y=m x+c is a tangent to the ellipse (x^(2))/(a^(2))...

    Text Solution

    |

  4. The equation of the normal to the hyperbola 3 x^(2)-y^(2)=3 at (2,-3) ...

    Text Solution

    |

  5. What does this equation x^2 - 4y^2 - 2x + 16y - 40 =0 represent?

    Text Solution

    |

  6. The centre of the hyperbola : 9x^2-36x-16y^2+96y-252=0 is

    Text Solution

    |

  7. The Asymptotes of the hyperbola 16x^2 - 9y^2 = 144 are

    Text Solution

    |

  8. The eccentricity of the rectangular hyperbola is

    Text Solution

    |

  9. The equation of the tangent to the curve: x^2-y^2-8x+2y+11=0 at (2,1)...

    Text Solution

    |

  10. The value of ' m ' for which y=mx+6 is a tangent to the hyperbola x^2/...

    Text Solution

    |

  11. The equation of the tangent to the hyperbola 4 y^(2)=x^(2)-1 at the po...

    Text Solution

    |

  12. If e and e^(prime) are eccentricities of a hyperbola its conjugate, th...

    Text Solution

    |

  13. The value of K so that y=4x+K may touch the hyperbola (x^(2))/(64)-(y^...

    Text Solution

    |

  14. The eccentricity of the hyperbola 36 x^(2)-25 y^(2)=900 is

    Text Solution

    |

  15. If P is any point on the hyperbola ((x-1)^(2))/(9)-((y+1)^(2))/(16)=1 ...

    Text Solution

    |

  16. The point of intersection of two perpendicular tangents to (x^(2))/(a^...

    Text Solution

    |

  17. The line p=x cos alpha+y sin alpha becomes tangent to (x^(2))/(a^(2))-...

    Text Solution

    |

  18. The eccentricity of the hyperbola (sqrt(1999))/(3)(x^(2)-y^(2))=1 is

    Text Solution

    |

  19. The product of the perpendicular from any poitn P(x,y) on the hyperbol...

    Text Solution

    |

  20. The length of transverse axis of the hyperbola 3x^(2) - 4y^(2) = 32 is

    Text Solution

    |