Statement 1 The tangent and normal at any point P on a ellipse bisect the external and internal angles between the focal distance of P.

If (-2,5) and (3,7) are the points of intersection of the tangent and normal at a point on a parabola with the axis of the parabola, then the focal distance of that point is

Statement 1 : If the line x+y=3 is a tangent to an ellipse with focie (4, 3) and (6,y) at the point (1, 2) then y=17. Statement 2 : Tangent and normal to the ellipse at any point bisect the angle subtended by the foci at that point.

Consider the ellipse whose major and minor axes are x-axis and y-axis, respectively. If phi is the angle between the CP and the normal at point P on the ellipse, and the greatest value tan phi is 3/4 (where C is the centre of the ellipse). Also semi-major axis is 10 units . The eccentricity of the ellipse is

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

The tangent and normal at any point P of an ellipse x^(2)/a^(2)+y^(2)/b^(2)=1 cut its major axis in point Q and R respectively. If QR=a prove that the eccentric angle of the point P is given by e^(2)cos^(2)phi+cosphi-1=0

The tagents at any point P of the circle x^(2)+y^(2)=16 meets the tangents at a fixed point A at T. Point is joined to B, the other end of the diameter, through, A. The sum of focal distance of any point on the curce is

If S be the focus of the parabola and tangent and normal at any point P meet its axis in T and G respectively, then prove that ST=SG = SP .

For the ellipse x^2/9+y^2/4=1 . Let O be the centre and S and S' be the foci. For any point P on the ellipse the value of (PS.PS'd^2)/9 (where d is the distance of O from the tangent at P) is equal to

If the least area of triangle formed by tangent,normal at any point P on the curve y = f(x) and X-axis is 4 sq. unit. Then the ordinate of the point P (P lies in first quadrant) is

If CF be the perpendicular from the centre C of the ellipse (x^(2))/(12)+(y^(2))/(8)=1 , on the tangent at any point P and G is the point where the normal at P meets the major axis, then the value of (CF*PG) equals to :