If S and S' are the foci of `x^2/16+y^2/25=1`, then show that PS+PS'=10, where P is any point on the ellipse.

S_1a n dS_2 are the foci of an ellipse of major axis of length 10 units, and P is any point on the ellipse such that the perimeter of triangle P S_1 is 15. Then the eccentricity of the ellipse is 0.5 (b) 0.25 (c) 0.28 (d) 0.75

Let d be the perpendicular distance from the centre of the ellipse x^2/a^2+y^2/b^2=1 to the tangent drawn at a point P on the ellipse. If F_1 & F_2 are the two foci of the ellipse, then show the (PF_1-PF_2)^2=4a^2(1-b^2/d^2) .

Let P be a point on the ellipse x^2/a^2+y^2/b^2=1 , 0 < b < a . Let the line parallel to y-axis passing through P meet the circle x^2 +y^2=a^2 at the point Q such that P and Q are on the same side of x-axis. For two positive real numbers r and s, find the locus of the point R on PQ such that PR : RQ = r : s and P varies over the ellipse.

P is any point on the hyperbola x^(2)-y^(2)=a^(2) . If F_1 and F_2 are the foci of the hyperbola and PF_1*PF_2=lambda(OP)^(2) . Where O is the origin, then lambda is equal to

Area bounded by the ellipse : x^2/16 + y^2/9 = 1 is :

The normal at a point P, on the ellipse x^2+4y^2=16 meets the x-axis at Q. If M is the mid-point of the line segment PQ, then the locus of M intersects the latus-rectum of the given ellipse at the points :

Triangles are formed by pairs of tangent drawn from any point on the ellipse a^(2)x^(2)+b^(2)y^(2)=(a^(2)+b^(2)) to the ellipse x^(2)/a^(2)+y^(2)/b^(2)=1 and the chord of contact. Show that the orthocentre of each such triangles lies triangle lies on the ellipse.

Let RS be the diameter of the circle x^2+y^2=1, where S is the point (1,0) Let P be a variable point (other than R and S ) on the circle and tangents to the circle at S and P meet at the point Q.The normal to the circle at P intersects a line drawn through Q parallel to RS at point E. then the locus of E passes through the point(s)-

C is the centre of the ellipse x^(2)/16+y^(2)/9=1 and A and B are two points on the ellipse such that /_ACB=90^@ , then 1/(CA)^(2)+1/((CB)^(2))=