Find the orthogonal trajectory of `y^2=4a x` (a being the parameter).

Find the orthogonal trajectories of family of curves x^2+y^2=c x

Find the equation of the common tangent of y^2=4a x and x^2=4a ydot

Two lines are drawn at right angles, one being a tangent to y^2=4a x and the other x^2=4b ydot Then find the locus of their point of intersection.

Find the area of the region bounded by y^2=4ax and x=|y| .

A variable parabola y^(2) = 4ax, a (where a ne -(1)/(4)) being the parameter, meets the curve y^(2) +x - 2 = 0 at two points. The locus of the point of intersecion of tangents at these points is

Find the range of parameter a for which a unique circle will pass through the points of intersection of the hyperbola x^2-y^2=a^2 and the parabola y=x^2dot Also, find the equation of the circle.

Find the range of parameter a for which a unique circle will pass through the points of intersection of the hyperbola x^2-y^2=a^2 and the parabola y=x^2dot Also, find the equation of the circle.

A binomial random variable X ·satisfies the reiation 9P(X = 4) = P(X =2) when n= 6. Find the parameter p.

The locus of the center of a circle which cuts orthogonally the parabola y^2=4x at (1,2) is a curve