Answer the following:Tangents to the circle `x^2+y^2=a^2`with inclinations,`theta_1`and `theta_2`intersect in P.Find the locus of point P such that`tantheta_1+tantheta_2=0`

Answer the following:Tangents to the circle x^2+y^2=a^2 with inclinations, theta_1 and theta_2 intersect in P.Find the locus of point P such that cottheta_1+cottheta_2=5

Answer the following:Tangents to the circle x^2+y^2=a^2 with inclinations, theta_1 and theta_2 intersect in P.Find the locus of point P such that cottheta_1.cottheta_2=c

Answer the following:Show that x=-1 is a tangent to the circle x^2+y^2-2y=0 at (-1,1)

Answer the following:Find the equation of tangent to the circle x^2+y^2=5 at the point (1,-2) on it.

Two tangents to the hyperbola x^2/a^2-y^2/b^2=1 make angles theta_1,theta_2 , with the transverse axis. Find the locus of their point of intersection if tantheta_1+tantheta_2=k .

Answer the following:Find the equation of tangent to the circle x^2+y^2=64 at the point ((2pi)/3)

Answer the following:If the tangent at (3,-4) to the circle x^2+y^2=25 touches the circle x^2+y^2+8x-4y+c=0 ,then find the value of c.

Answer the following: Find the equation of tangent to the circle x=5costheta and y=5sintheta at the point theta=pi/3 on it.

P and Q are two points on the ellipse x^2/a^2+y^2/b^2=1 with eccentric angles theta_1 and theta_2 . Find the equation of the locus of the point of intersection of the tangents at P and Q if theta_1+theta_2=pi/2 .

Answer the following:Find the equation of tangent to circle x^2+y^2-6x-4y=0 ,at the point (6,4) on it.