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

`(a^(2))/(x^(2))+(b^(2))/(y^(2))=1`

B

`(a^(2))/(x^(2))+(b^(2))/(y^(2))=2`

C

`(x^(2))/(a^(2))+(y^(2))/(b^(2))=4`

D

`(a^(2))/(x^(2))+(b^(2))/(y^(2))=4`

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

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 .