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.

If the point (x,y) is equidistant from the points (2,-1) and (-3,4) , then show that , y=x+2 .

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 . Find the point of intersection of these tangents.

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.

Through a fixed point (h, k) secants are drawn to the circle x^2 +y^2 = r^2 . Then the locus of the mid-points of the secants by the circle 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.

If the tangents are drawn to the circle x^2+y^2=12 at the point where it meets the circle x^2+y^2-5x+3y-2=0, then find the point of intersection of these tangents.

The length of the tangent of the circle x^2+y^2-2x-y -7 = 0 from the point (-1,-3) is

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 (a) 2x-y+10=0 (b) 2x+y-10=0 (c) x-2y+10=0 (d) 2x+y-10=0

From the origin, chords are drawn to the circle (x-1)^2 + y^2 = 1 . The equation of the locus of the mid-points of these chords