Tangents are drawn to the circle `x^(2)+y^(2)=a^(2)` from two points on the x-axis , equidistant from the point (k,0). Show that the locus of their point of intersection is `ky^(2)=a^(2)(k-x)`.

Tangents are drawn to the circle x^2+y^2=a^2 from two points on the axis of x , equidistant from the point (k ,0)dot Show that the locus of their intersection is k y^2=a^2(k-x)dot

Tangents are drawn to the hyperbola 3x^2-2y^2=25 from the point (0,5/2)dot Find their equations.

Tangents are drawn to the hyperbola 3x^2-2y^2=25 from the point (0,5/2)dot Find their equations.

Determine the point on x-axis which is equidistant from the points (-2,3,5) and (1,2,3) .

From a point on the circle x^2+y^2=a^2 , two tangents are drawn to the circle x^2+y^2=b^2(a > b) . If the chord of contact touches a variable circle passing through origin, show that the locus of the center of the variable circle is always a parabola.

Tangent are drawn to the circle x^2+y^2=1 at the points where it is met by the circles x^2+y^2-(lambda+6)x+(8-2lambda)y-3=0,lambda being the variable. The locus of the point of intersection of these tangents is

Tangents PA and PB are drawn to the circle x^2 +y^2=8 from any arbitrary point P on the line x+y =4 . The locus of mid-point of chord of contact AB is

The tangent to y^(2)=ax make angles theta_(1)andtheta_(2) with the x-axis. If costheta_(1)costheta_(2)=lamda , then the locus of their point of intersection is

A tangent is drawn to each of the circles x^2+y^2=a^2 and x^2+y^2=b^2dot Show that if the two tangents are mutually perpendicular, the locus of their point of intersection is a circle concentric with the given circles.

Tangents are drawn to the circle x^2+y^2=9 at the points where it is met by the circle x^2+y^2+3x+4y+2=0 . Fin the point of intersection of these tangents.