At the point of intersection of the curves `y^2=4ax" and "xy=c^2`, the tangents to the two curves make angles `alpha" and "beta` respectively with x-axis. Then `tan alpha cot beta=`

If the normal at two points of the parabola y^2 = 4ax , meet on the parabola and make angles alpha and beta with the positive directions of x-axis, then tanalpha tanbeta = (A) -1 (B) -2 (C) 2 (D) a

The locus of the point through which pass three normals to the parabola y^2=4ax , such that two of them make angles alpha&beta respectively with the axis & tanalpha *tanbeta = 2 is (a > 0)

At the point of intersection of the rectangular hyperbola xy=c^2 and the parabola y^2=4ax tangents to the rectangular hyperbola and the parabola make angles theta and phi , respectively with x-axis, then

Write the coordinates of the point on the curve y^2=x where the tangent line makes an angle pi/4 with x-axis.

The locus of the point of intersection of the tangents to the parabola y^2 = 4ax which include an angle alpha is

If the lines px^2-qxy-y^2=0 makes the angles alpha and beta with X-axis , then the value of tan(alpha+beta) is

If the curves y= a^(x) and y=e^(x) intersect at and angle alpha, " then " tan alpha equals

alpha and beta are acute angles and cos2alpha = (3cos2beta-1)/(3-cos2beta) then tan alpha cot beta =

The acute angles between the curves y=2x^(2)-x and y^(2)=x at (0, 0) and (1, 1) are alpha and beta respectively, then

The locus of the point of intersection of two tangents to the parabola y^(2)=4ax which make the angles theta_(1) and theta_(2) with the axis so that cot theta_(1)+cot theta_(2) = c is