Let `F1,F_2` be two focii of the ellipse and `PT and PN` be the tangent and the normal respectively to the ellipse at ponit P.then

Let F_1,F_2 be two foci of the ellipse x^2/(p^2+2)+y^2/(p^2+4)=1 . Let P be any point on the ellipse , the maximum possible value of PF_1 . PF_2 -p^2 is

Ellipse elements, Tangent and Normal

S (3, 4) and S^(') (9, 12) are the focii of an ellipse and the foot of the perpendicular from S to a tangent to the ellipse is (1, -4). Then the eccentricity of the ellipse is

Let F_1(x_1,0) and F_2(x_2,0), for x_1 0, be the foci of the ellipse x^2/9+y^2/8=1 Suppose a parabola having vertex at the origin and focus at F_2 intersects the ellipse at point M in the first quadrant and at point N in the fourth quadrant. If the tangents to the ellipse at M and N meet at R and the normal to the parabola at M meets the x-axis at Q, then the ratio of area of the triangle MQR to area of the quadrilateral MF_1 NF_2 is

Let F_1(x_1,0)" and "F_2(x_2,0) , for x_1 lt 0 " and" x_2 gt 0 , be the foci of the ellipse (x^2)/(9)+(y^2)/(8)=1 . Suppose a parabola having vertex at the origin and focus at F_2 intersects the ellipse at point M in the first quadrant and at point N in the fourth quadrant. If the tangents to the ellipse at M and N meet at R and the normal to the parabola at M meets the x-axis at Q, then the ratio of the area of the triangle MQR to area of the quadrilateral MF_1NF_2 is :

If F_1 (-3, 4) and F_2 (2, 5) are the foci of an ellipse passing through the origin, then the eccentricity of the ellipse is

Let A(3.2) and B(4,7) are the foci of an ellipse and the line x+y-2=0 is a tangent to the ellipse,then the point of contact of this tangent with the ellipse is

Let P be an arbitrary point on the ellipse (x^(2))/(a^(2)) + (y^(2))/(b^(2)) = 1, a gt b gt 0 . Suppose F_(1) and F_(2) are the foci are the ellipse. The locus of the centroid of the triangle PF_(1)F_(2) as P moves on the ellipse is- (A) a circle (B) a parabola (C) an ellipse (D) a hyperbola