In the given figure, triangle ABC is circumscribing a circle. Find the length of BC, if AF=3 cm, FB=4 cm and AC= 9 cm
If F1 and F2 are the feet of the perpendiculars from the foci S1andS2 of the ellipse 25x2+16y2=1 on the tangent at any point P on the ellipse, then prove that S1F1+S2F2≥8.
An ellipse has OB as the semi-minor axis, FandF′ as its foci, and ∠FBF′ a right angle. Then, find the eccentricity of the ellipse.
If the tangent to the ellipse x2+2y2=1 at point P(21,21) meets the auxiliary circle at point RandQ , then find the points of intersection of tangents to the circle at QandR˙
The tangent at a point P on an ellipse intersects the major axis at T,andN is the foot of the perpendicular from P to the same axis. Show that the circle drawn on NT as diameter intersects the auxiliary circle orthogonally.
Find the equation of the parabola that satisfies the following conditions: Vertex (0,0) passing through (2,3) and axis is along x-axis