Home
Class 12
MATHS
The length of the tangent of the ellipse...

The length of the tangent of the ellipse `x^2/25+y^2/16=1` intercepted between auxiliary circle such that the portionof the tangent intercepted between the auxiliary circle subtends equal angles at foci is

A

6

B

3

C

4

D

8

Text Solution

Verified by Experts


Let AB be the length of the tangent intercepted by auxiliary circle and `S_(1),S_(2)` be the foci.
Given that
`angleAS_(1)B=angleAS_(2)B`
`rArrangleS_(1)AB=angleS_(2)AB=(pi)/(2)`
So `AS_(1)S_(2)B` is a rectangle.
`:. AB=S_(1)S_(2)=2aex=2xx5xx(3)/(5)=6`
Promotional Banner

Similar Questions

Explore conceptually related problems

For the curve x y=c , prove that the portion of the tangent intercepted between the coordinate axes is bisected at the point of contact.

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 .

The length of the tangent of the circle x^2+y^2-2x-y -7 = 0 from the point (-1,-3) is

Show that the circle with the portion of the line 3x + 4y = 12 intercepted between the axes as diameter, passes through the origin.

Show that the circle with the portion of the line 3x + 4y = 12 intercepted between the axes as diameter passes through the origin.

If the tangent to the ellipse x^2+2y^2=1 at point P(1/(sqrt(2)),1/2) meets the auxiliary circle at point R and Q , then find the points of intersection of tangents to the circle at Q and Rdot

Show that the circle with the portion of the line 3x + 4y = 12 intercepted between the axes as diameter , passes through the origin .

The exhaustive set of values of alpha^2 such that there exists a tangent to the ellipse x^2+alpha^2y^2=alpha^2 and the portion of the tangent intercepted by the hyperbola alpha^2x^2-y^2=1 subtends a right angle at the center of the curves is:

Two perpendicular tangents drawn to the ellipse (x^2)/(25)+(y^2)/(16)=1 intersect on the curve.

Find the middle point of the chord of the circle x^2+y^2=25 intercepted on the line x-2y=2