From an external point `P ,` a pair of tangents is drawn to the parabola `y^2=4xdot` If `theta_1a n dtheta_2` are the inclinations of these tangents with the x-axis such that `theta_1+theta_2=pi/4` , then find the locus of `Pdot`

Two tangents are drawn from the point (-2,-1) to the parabola y^(2)=4x .If theta is the angle between these tangents,then the value of tan theta is

From a point P tangents are drawn to the parabola y^2=4ax . If the angle between them is (pi)/(3) then locus of P is :

From an external point P, tangents are drawn to the parabola. Find the equation of the locus of P when these tangents make angles theta_(1)andtheta_(2) with the axis of the parabola such that costheta_(1)costheta_(2)=mu , where mu is a constant.

Find the equation of the tangent to the curve x=theta+sin theta,y=1cos theta at theta=(pi)/(4)

Find the equation of the tangent to the curve x=theta+sintheta , y=1+costheta at theta=pi//4 .

Tangents are drawn to the parabola y^2=12x at the points A, B and C such that the three tangents form a triangle PQR. If theta_1,theta_2 and theta_3 be the inclinations of these tangents with the axis of x such that their cotangents form an arithmetical progression (in the same order) with common difference 2. Find the area of the triangle PQR.

If theta_(1),theta_(2) be the inclinations of tangents drawn from point P to the circle x^(2)+y^(2)=a^(2) such that cot theta_(1)+cot theta_(2)=k

Find the equations of tangent to the curve x=1-cos theta,y=theta-sin theta at theta=(pi)/(4)

The inclination of the tangent at theta=(pi)/(3) on the curve x=a(theta+sin theta) , y=a(1+cos theta) is