Home
Class 12
MATHS
An ellipse has point (1,-1)a n d(2,-1) a...

An ellipse has point `(1,-1)a n d(2,-1)` as its foci and `x+y-5=0` as one of its tangents. Then the point where this line touches the ellipse is `((32)/9,(22)/9)` (b) `((23)/9,2/9)` `((34)/9,(11)/9)` (d) none of these

Text Solution

Verified by Experts


Image of focus S(2,-1) in the tangennt at P in the tangent at P is lies on the line S'P
Let image `S'''-=(h,k)`
`:. (h-2)/(1)=(k+1)/(1)=(2(2-2-5))/(2)=4`
`rArr S'''=(6,3)`
Equation of line SS'' is
4x-5y=9
Soving tangent and SS'' , we get `P-=((34)/(9),(11)/(9))`
Promotional Banner

Similar Questions

Explore conceptually related problems

An ellipse has the points (1, -1) and (2,-1) as its foci and x + y = 5 as one of its tangent then the value of a^2+b^2 where a,b are the lenghta of semi major and minor axes of ellipse respectively is :

Find the area of the region bounded by the ellipse x^(2)/4+y^(2)/9=1 .

Find the number of rational points on the ellipse (x^2)/9+(y^2)/4=1.

Find the area of the region bounded by the ellipse x^(2)/16+y^(2)/9=1 .

find the length of the latus rectum of the ellipse (x^(2))/(9) +(y^(2))/(16) = 1

Dentermine the position of the point (2,-3) with respect to the ellipse (x^(2))/(9) +(y^(2))/(25) = 1 .

Find the equations of the tangents drawn from the point (2, 3) to the ellipse 9x^2+16 y^2=144.

The normal to the curve 2x^2+y^2=12 at the point (2,2) cuts the curve again at (A) (-(22)/9,-2/9) (B) ((22)/9,2/9) (C) (-2,-2) (D) none of these

Find the point on the hyperbola x^2-9y^2=9 where the line 5x+12 y=9 touches it.

Find the equation of the tangent at the specified points to each of the following curves. the ellipse 9x^(2)+16y^(2)=288 at (4,3)