If PN be the Perpendicular to the Major axis from P on ellipse and the tangent at P meet the x axis in T. If C is the centre of the ellipse `x^2/a^2 + y^2/b^2 = 1` then show that CT . CN ` = a^(2)`

P is a point on the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 , N is the foot of the perpendicular from P on the transverse axis. The tangent to the hyperbola at P meets the transverse axis at T . If O is the centre of the hyperbola, then OT . ON is equal to

P is a point on the hyperbola (x^(2))/(y^(2))-(y^(2))/(b^(2))=1 , and N is the foot of the perpendicular from P on the transverse axis. The tantent to the hyperbola at P meets the transverse axis at T. If O is the centre of the hyperbola, then OT.ON is equal to

P is a point on the hyperbola x^2/a^2-y^2/b^2=1 ; N is a foot of perpendicular from P on the transverse axis . The tangent to hyperbola at P meets the transeverse axis at T . If O is the center of the hyperbola ; then find the value of OTxxON.

If the length of the major axis intercepted between the tangent and normal at a point P (a cos theta, b sin theta) on the ellipse (x^(2))/(a^(2)) +(y^(2))/(b^(2)) =1 is equal to the length of semi-major axis, then eccentricity of the ellipse is

The length ofthe normal (terminated by the major axis) at a point of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 is

If P is a point on the hyperbola (x^(2))/(7)-(y^(2))/(3)=1 and N is the foot of perpendicular from P on the transverse axis. The tangent to the hyperbola at P meets the transverse axis at T. If O is the centre of hyperbola,then OT.ON=(A)4(B)7(C)3 (D) 10

The locus of the foot of the perpendicular from the foci an any tangent to the ellipse x^(2)/a^(2) + y^(2)/b^(2) = 1 , is

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.

A focal chord perpendicular to major axis of the ellipse 9x^(2)+5y^(2)=45 cuts the curve at P and Q then length of PQ is