Consider any point P on the ellipse `x^2/a^2+y^2/b^2=1(a < b)`. Prove that the greatest value of the tangent of the angle between OP and the normal at P is `(a^2-b^2)/(2ab)` ,where O is the origin.

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 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 .

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

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 N is the foot of the perpendicular drawn from any point P on the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 (a>b) to its major axis AA' then (PN^(2))/(AN A'N) =

Number of points on the ellipse x^2/a^2+y^2/b^2=1 at which the normal to the ellipse passes through at least one of the foci of the ellipse is

If "N" is the foot of the perpendicular drawn from any point "P" on the ellipse " (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 (a>b)" to its major axis " A A^(1) " then (PN^(2))/(ANA^(1)N) =

P_1(theta_1) and P_2(theta_2) are two points on the ellipse x^2/a^2+y^2/b^2=1 such that tan theta_1 tan theta_2 = (-a^2)/b^2 . The chord joining P_1 and P_2 of the ellipse subtends a right angle at the

Consider any P on the ellipse x^(2)/25+y^(2)/9=1 in the firsty quadrant. Let r and then (r + s) is equal to

If SK be the perpendicular from the focus s on the tangent at any point P on the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1(a>b). then locus of K is