Find the maximum area of the ellipse a2x2+b2y2=1 which touches the line y=3x+2.
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 P divides OA internally in the ratio λ1:λ2 and Q divides OA externally in the ratio λ1;λ2, then prove that OA is the harmonic mean of OP and OQ˙
If ABC having vertices A(acosθ1,asinθ1),B(acosθ2asinθ2),andC(acosθ3,asinθ3) is equilateral, then prove that cosθ1+cosθ2+cosθ3=sinθ1+sinθ2+sinθ3=0.
Prove that the area of the triangle whose vertices are (t,t−2),(t+2,t+2), and (t+3,t) is independent of t˙