If y, is ordinate of a point P on the ellipse then show that the angle between its focal radius and tangent at it, is `tan^-1 (b^2/(aey_1))`

Tangents are drawn to the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1,(a > b), and the circle x^2+y^2=a^2 at the points where a common ordinate cuts them (on the same side of the x-axis). Then the greatest acute angle between these tangents is given by (A) tan^(-1)((a-b)/(2sqrt(a b))) (B) tan^(-1)((a+b)/(2sqrt(a b))) (C) tan^(-1)((2a b)/(sqrt(a-b))) (D) tan^(-1)((2a b)/(sqrt(a+b)))

Let P be any point on a directrix of an ellipse of eccentricity e,S be the corresponding focus,and C the center of the ellipse.The line PC meets the ellipse at A. The angle between PS and tangent a A is alpha. Then alpha is equal to tan^(-1)e( b) (pi)/(2)tan^(-1)(1-e^(2))( d) none of these

Which of the following is/are true about the ellipse x^2+4y^2-2x-16 y+13=0? the latus rectum of the ellipse is 1. The distance between the foci of the ellipse is 4sqrt(3)dot The sum of the focal distances of a point P(x , y) on the ellipse is 4. Line y=3 meets the tangents drawn at the vertices of the ellipse at points P and Q . Then P Q subtends a right angle at any of its foci.

Prove that the tangent and normal at any point of an ellipse bisect the external and internal angles between the focal distances of the point

If y_(1),y_(2) are the ordinates of two points P and Q on the parabola and y_(3) is the ordinate of the intersection of tangents at P and Q, then

Find the points on the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 such that the tangent at each point makes equal angles with the axes.

Find the angle between the pair of tangents from the point (1,2) to the ellipse 3x^(2)+2y^(2)=5