Let `5x-3y=8sqrt2` be normal at `P(5/(sqrt(2)),3/(sqrt(2)))` to an ellipse `(x^2)/(a^2)+(y^2)/(b^2)=1, a > b.` If `m,m'` are feet of perpendiculars from foci `s,s'` respectively. or tangents at p, then point of intersection of `sm' and s'm` is

If a normal at any point on the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1(a gt b) meet the major and minor axes at M and N respectively, such that (P M)/(P N)=(2)/(3) , then the eccentricity =

If sqrt(3) b x+a y=2 a b is a tangent to the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 then the eccentric angle of the point is

If M_(1) and M_(2) are the feet of perpendiculars from foci F_(1) and F_(2) of the ellipse (x^(2))/(64)+(y^(2))/(25)=1 on the tangent at any point P of the ellipse then

Consider an ellipse x^2/25+y^2/9=1 with centre c and a point P on it with eccentric angle pi/4. Nomal drawn at P intersects the major and minor axes in A and B respectively. N_1 and N_2 are the feet of the perpendiculars from the foci S_1 and S_2 respectively on the tangent at P and N is the foot of the perpendicular from the centre of the ellipse on the normal at P. Tangent at P intersects the axis of x at T.

Let P be a point on the ellipse x^2/100 + y^2/25 =1 and the length of perpendicular from centre of the ellipse to the tangent to ellipse at P be 5sqrt(2) and F_1 and F_2 be the foci of the ellipse, then PF_1.PF_2 .

Let P be a point on the ellipse x^2/100 + y^2/25 =1 and the length of perpendicular from centre of the ellipse to the tangent to ellipse at P be 5sqrt(2) and F_1 and F_2 be the foci of the ellipse, then PF_1.PF_2 .

If F_(1) and F_(2) are the feet of the perpendiculars from foci s_(1) and s_(2) of an ellipse 3x^(2)+5y^(2)=15 on the tangent at any point P on the ellipse then (s_(1)F_(1))(S_(2)F_(2)) =