Home
Class 12
MATHS
Prove that the focus of id-points of the...

Prove that the focus of id-points of the portion of the tamgents to the ellipse `x^(2)/a^(2)+y^(2)/b^(2)=1` intercepted between the axes is a `a^(2)y^(2)+b^(2)x^(2)=4x^(2)y^(2)`.

A

`4x^2y^2=a^2x^2-b^2y^2`

B

`2x^2y^2=a^2y^2-b^2x^2`

C

`x^2y^2=a^2y^2-b^2x^2`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • CONIC SECTIONS

    VMC MODULES ENGLISH|Exercise Numerical Value Type for JEE Main|15 Videos
  • CONIC SECTIONS

    VMC MODULES ENGLISH|Exercise JEE MAIN ARCHIVE|15 Videos
  • CONIC SECTIONS

    VMC MODULES ENGLISH|Exercise LEVEL - 1|178 Videos
  • COMPLEX NUMBERS

    VMC MODULES ENGLISH|Exercise JEE ARCHIVE|76 Videos
  • DIFFERENTIAL CALCULUS

    VMC MODULES ENGLISH|Exercise JEE Advanced (Archive)|75 Videos

Similar Questions

Explore conceptually related problems

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 axes is the curve

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

show that the locus of the middle points of portions of the tangents to the hyperbola x^2/a^2 - y^2/b^2 = 1 intercepted between the axes is 4x^2 y^2 = a^2 y^2 - b^2 x^2 .

If the tangent to the ellipse x^(2)/a^(2) + y^(2)/b^(2) = 1 makes intercepts p and q on the coordinate axes, then a^(2)/p^(2) + b^(2)/q^(2) =

The locus of the middle points of the portions of the tangents of the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 included between the axis is the curve (a)    (x^2)/(a^2)+(y^2)/(b^2)=1/4 (b)    (a^2)/(x^2)+(b^2)/(y^2)=4 (c)    a^2x^2+b^2y^2=4 (d)    b^2x^2+a^2y^2=4

The locus of mid points of parts in between axes and tangents of ellipse x^2/a^2 + y^2/b^2 =1 will be

The distance of the point 'theta' on the ellipse x^(2)/a^(2) + y^(2)/b^(2) = 1 from a focus, is

The line x = at^(2) meets the ellipse x^(2)/a^(2) + y^(2)/b^(2) = 1 in the real points iff

Show that the tangents at the ends of conjugate diameters of the ellipse x^(2)/a^(2)+y^(2)/b^(2)=1 intersect on the ellipse x^(2)/a^(2)+y^(2)/b^(2)=2 .

If any tangent to the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 intercepts equal lengths l on the axes, then find l .

VMC MODULES ENGLISH-CONIC SECTIONS-LEVEL - 2
  1. If P(a sec alpha,b tan alpha)" and "Q(a sec beta, b tan beta) are two ...

    Text Solution

    |

  2. If x+iy=sqrt(phi+iy), where i=sqrt(-1)" and "phi and Psi are non-zero ...

    Text Solution

    |

  3. If a ray of light incident along the line 3x+(5-4sqrt2)y=15 gets refle...

    Text Solution

    |

  4. At the point of intersection of the rectangular hyperbola xy = c^(2) a...

    Text Solution

    |

  5. If p ,q ,r ,s ae rational numbers and the roots of f(x)=0 are eccentri...

    Text Solution

    |

  6. If from the point (alpha,alpha^2) two tangents drawn to any one branch...

    Text Solution

    |

  7. Consider a hyperbola xy = 4 and a line y = 2x = 4. O is the centre of ...

    Text Solution

    |

  8. If theta is eliminated from the equations a sec theta-x tan theta=y" a...

    Text Solution

    |

  9. If A hyperbola be rectangular and its equation be xy=c^(2), prove tha...

    Text Solution

    |

  10. The normal at P(ct,(c )/(t)) to the hyperbola xy=c^2 meets it again a...

    Text Solution

    |

  11. Chords of the hyperbola x^2/a^2-y^2/b^2=1 are tangents to the circle d...

    Text Solution

    |

  12. Two rods of lengths aa n db slide along the x- and y-axis , respective...

    Text Solution

    |

  13. Show that the acute angle between the asymptotes of the hyperbola (x^2...

    Text Solution

    |

  14. the product of the perpendicular distance from any points on a hyperbo...

    Text Solution

    |

  15. Prove that the perpendicular focal chords of a rectangular hyperbola a...

    Text Solution

    |

  16. If a variable line has its intercepts on the coordinate axes ea n de^(...

    Text Solution

    |

  17. Tangents are drawn to hyperbola (x^2)/(16)-(y^2)/(b^2)=1. (b being par...

    Text Solution

    |

  18. A straight line through the point (1,1) meets the X-axis at A and Y-ax...

    Text Solution

    |

  19. The line lx + my+n=0 will be a normal to the hyperbola b^2x^2-a^2y^2...

    Text Solution

    |

  20. Prove that the focus of id-points of the portion of the tamgents to th...

    Text Solution

    |