Tangent lines are drawn at the points P and Q where f''(x) vanishes for the function f(x)=cos x on `[0,2pi]` The tangent lines at P and Q intersect each other at R so as to form a triangle PQR. If area triangle PQR is `kpi^(2)` then find the value of 36k.

Lines x+y=1 and 3y=x+3 intersect the ellipse x^(2)+9y^(2)=9 at the points P,Q,R. the area of the triangles PQR is

Consider the curves C_(1):|z-2|=2+Re(z) and C_(2):|z|=3 (where z=x+iy,x,y in R and i=sqrt(-1) .They intersect at P and Q in the first and fourth quadrants respectively.Tangents to C_(1) at P and Q intersect the x- axis at R and tangents to C_(2) at P and Q intersect the x -axis at S .If the area of Delta QRS is lambda sqrt(2) ,then find the value of (lambda)/(2)

Let the line y = mx intersects the curve y^2 = x at P and tangent to y^2 = x at P intersects x-axis at Q. If area ( triangle OPQ) = 4, find m (m gt 0) .

Tangents are drawn from the point (-1,2) to the parabola y^(2)=4x. These tangents meet the line x=2 at P and Q, then length of PQ is

From the point (3 0) 3- normals are drawn to the parabola y^2 = 4x . Feet of these normal are P ,Q ,R then area of triangle PQR is

The triangle PQR of which the angles P,Q,R satisfy cos P = (sin Q)/(2 sin R ) is :

A line is drawn through the point (1,2) to meet the coordinate axes at P and Q such that it forms a triangle OPQ ,where 0 is the origin.If the area of the triangle OPQ is least,the slope of the line PQ is k ,then |k| =

Normal at a point P(a,-2a) intersects the parabola y^(2)=4ax at point Q.If the tangents at P and Q meet at point R if the area of triangle PQR is (4a^(2)(1+m^(2))^(3))/(m^(lambda)). Then find lambda