Orthocenter

Q. Let sin-1x + sin-1y = sin-1(x√1-y^2 + y√1-x^2) then find the area represented by the locus of point (x, y) if |x|<=1 , |y|<=1

Q. If x, y, z are the distances of the vertices of triangle ABC from its orthocenter, then x+y+z = .

1. r+R
2. 2(r+R)
3. 2r+R
4. r+2R

Q. Find the length of the perpendicular from the origin to the straight line joining the two points whose coordinates are (a cos α, a sin α) and (a cos β, a sin β).

Q. the locus of a point P which divides the line segment joining(1, 0) and (2costheta, 2 sintheta) internally in the ratio 1:2 for all theta is a

Q. 16. The equation (5+3)sin thita + (5-3)cos thita =3sin alpha holds for (A) two pair of value of (thita, alpha). (B) three pairs of (thita, alpha). (C) just one pairs of (thita, alpha). (D) infinitely pairs of (thita, alpha)