Home
Class 12
MATHS
If the normal at any point P on the elli...

If the normal at any point `P` on the ellipse `x^2/a^2 + y^2/b^2 = 1` cuts the major and minor axes in `L and M` respectively and if `C` is the centre of the ellipse , then `a^2\ CL^2 + b^2\ CM^2` is equal to
(A) `(a-b)` (B) `(a^2 - b^2)^2` (C) `(a+b)` (D) `(a^2 + b^2)`

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • ELLIPSE

    ARIHANT MATHS ENGLISH|Exercise Exercise For Session 3|14 Videos

  • ELLIPSE

    ARIHANT MATHS ENGLISH|Exercise Exercise (Single Option Correct Type Questions)|30 Videos

  • ELLIPSE

    ARIHANT MATHS ENGLISH|Exercise Exercise For Session 1|18 Videos

  • DY / DX AS A RATE MEASURER AND TANGENTS, NORMALS

    ARIHANT MATHS ENGLISH|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|7 Videos

  • ESSENTIAL MATHEMATICAL TOOLS

    ARIHANT MATHS ENGLISH|Exercise Exercise (Single Integer Answer Type Questions)|3 Videos

Similar Questions

Explore conceptually related problems

If the normal at any point P of the ellipse x^2/a^2 + y^2/b^2 = 1 meets the major and minor axes at G and E respectively, and if CF is perpendicular upon this normal from the centre C of the ellipse, show that PF.PG=b^2 and PF.PE=a^2 .

The tangent at point P on the ellipse x^(2)/a^(2) + y^(2)/b^(2) = 1 cuts the minor axis in Q and PR is drawn perpendicular to the minor axis. If C is the centre of the ellipse, then CQ*CR =

If the normal at point P (theta) on the ellipse x^2/a^2 + y^2/b^2 = 1 meets the axes of x and y at M and N respectively, show that PM : PN = b^2 : a^2 .

If normal at any poin P on the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 (agtbgt0) meets the major and minor axes at Q and R, respectively, so that 3PQ=2PR, then find the eccentricity of ellipse

If normal at any point P to ellipse (x^2)/(a^2) + (y^2)/(b^2) = 1(a > b) meet the x & y axes at A and B respectively. Such that (PA)/(PB) = 3/4 , then eccentricity of the ellipse is:

If the normal at any point P on ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2)) =1 meets the auxiliary circle at Q and R such that /_QOR = 90^(@) where O is centre of ellipse, then

A tangent having slope of -4/3 to the ellipse (x^2)/(18)+(y^2)/(32)=1 intersects the major and minor axes at points A and B , respectively. If C is the center of the ellipse, then find area of triangle A B Cdot

If the normal at any point P on the ellipse x^2/a^2+y^2/b^2=1 meets the axes at G and g respectively, then find the ratio PG:Pg . (a) a : b (b) a^2 : b^2 (c) b : a (d) b^2 : a^2

If a tangent to the ellipse x^2/a^2+y^2/b^2=1 , whose centre is C, meets the major and the minor axes at P and Q respectively then a^2/(CP^2)+b^2/(CQ^2) is equal to

The tangent to x^(2)//a^(2)+y^(2)//b^(2)=1 meets the major and minor axes in P and Q respectively, then a^(2)//CP^(2)+b^(2)//CQ^(2)=