Find the eccentricity of an ellipse a2x2+b2y2=1 whose latus rectum is half of its major axis. (a>b)
Find the coordinates of the foci and the vertices, the eccentricity, the length of the latus rectum of the hyperbolas:(i) 9x2−16y2=1 (ii) y2−16x2=1
Angle of a line with the positive direction of the x-axis is θ . The line is rotated about some point on it in anticlockwise direction by angle 450 and its slope becomes 3. Find the angle θ˙
A tangent PQ at a point P of a circle of radius 5 cm meets a line through the centre O at a point Q so that OQ=12 cm. Length PQ is :
(A) 12 cm (B) 13 cm (C) 8.5 cm (D) 119cm.
The vertices of a triangle are A(−1,−7),B(5,1)andC(1,4)˙ If the internal angle bisector of ∠B meets the side AC in D, then find the length AD˙
If the point (x,−1),(3,y),(−2,3),and(−3,−2) taken in order are the vertices of a parallelogram, then find the values of xandy˙