The tangent at a point `P` on an ellipse intersects the major axis at `T ,a n dN` is the foot of the perpendicular from `P` to the same axis. Show that the circle drawn on `N T` as diameter intersects the auxiliary circle orthogonally.

the tangent at any point P on the ellipe x^(2)/6 + y^(2)/3 = 1 whose centre C meets the major axis at T and PN is the perpendicular to the major axis. The CN CT = _____

The tangent at any point P onthe parabola y^2=4a x intersects the y-axis at Qdot Then tangent to the circumcircle of triangle P Q S(S is the focus) at Q is

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 center of the hyperbola the OT.ON is equal to:

If the chord of contact of tangents from a point P to a given circle passes through Q , then the circle on P Q as diameter.

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

Statement 1 : For the ellipse (x^2)/5+(y^2)/3=1 , the product of the perpendiculars drawn from the foci on any tangent is 3. Statement 2 : For the ellipse (x^2)/5+(y^2)/3=1 , the foot of the perpendiculars drawn from the foci on any tangent lies on the circle x^2+y^2=5 which is an auxiliary circle of the ellipse.

The tangent at any point on the ellipse 16x^(2)+25y^(2) = 400 meets the tangents at the ends of the major axis at T_(1) and T_(2) . The circle on T_(1)T_(2) as diameter passes through

The chord of contact of tangents from a point P to a circle passes through Qdot If l_1a n dl_2 are the length of the tangents from Pa n dQ to the circle, then P Q is equal to

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 transvers axis at Tdot If O is the center of the hyperbola, then find the value of O TxO Ndot