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

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`.

Promotional Banner

Similar Questions

Explore conceptually related problems

If the normal at a point P on the ellipse (x^(2))/(144)+(y^(2))/(16)=1 cuts major and minor axes at Q and R respectively.Then PR:PQ is equal to

If the normal at any point P on the ellipse cuts the major and minor axes in G and g respectively and C be the centre of the ellipse, then

If the normal at any point P on the ellipse x^2/64+y^2/36=1 meets the major axis at G_1 and the minor axis at G_2 then the ratio of PG_1 and PG_2 is equal to

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

For the ellipse 4(x-2y+1)^(2)+9(2x+y+2)^(2)=180 lengths of major and minor axes are respectively

If the normal at P(theta) on the ellipse x^(2)/a^(2)+y^(2)/b^(2)=1 with focus S ,meets the major axis in G. then SG=

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 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, then a^2 CL^2 + b^2 CM^2 = (A) (a-b) (B) (a^2 - b^2) (C) (a+b) (D) (a^2 + b^2)

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 raio PG:Pg= (a) a:b(b)a^(2):b^(2)(c)b:a(d)b^(2):a^(2)