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)`.

The point of intersection of the curves y^(2) = 4x and the line y = x is

Consider the circle x^2+y^2=9 and the parabola y^2=8x . They intersect at P and Q in the first and fourth quadrants, respectively. Tangents to the circle at P and Q intersect the X-axis at R and tangents to the parabola at P and Q intersect the X-axis at S. The ratio of the areas of trianglePQS" and "trianglePQR is

If the line x-y-1=0 intersect the parabola y^(2)=8x at P and Q, then find the point on intersection of tangents P and Q.

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)

If line x-2y-1=0 intersects parabola y^(2)=4x at P and Q, then find the point of intersection of normals at P and Q.

If line x-2y-1=0 intersects parabola y^(2)=4x at P and Q, then find the point of intersection of normals at P and Q.

If line x-2y-1=0 intersects parabola y^(2)=4x at P and Q, then find the point of intersection of normals at P and Q.

If line x-2y-1=0 intersects parabola y^(2)=4x at P and Q, then find the point of intersection of normals at P and Q.

If line x-2y-1=0 intersects parabola y^(2)=4x at P and Q, then find the point of intersection of normals at P and Q.

A line y=2x+c intersects the circle x^(2)+y^(2)-2x-4y+1=0 at P and Q. If the tangents at P and Q to the circle intersect at a right angle,then |c| is equal to