Obtain the locus of the point of intersection of the tangent to the circle `x^2 + y^2 = a^2` which include an angle `alpha`.

The locus of the point of intersection of the tangents to the circle x^2+ y^2 = a^2 at points whose parametric angles differ by pi/3 .

Find the locus of the point of intersection of the perpendicular tangents of the curve y^2+4y-6x-2=0 .

Find the point(s) of intersection of the line 2x + 3y = 18 and the circle x^2 + y^2 = 25

The equations of the tangents to the circle x^2 + y^2 = 25 which are inclined at an angle of 30^@ to the x- axis are

If the straight line x - 2y + 1 = 0 intersects the circle x^2 + y^2 = 25 at points P and Q, then find the coordinates of the point of intersection of the tangents drawn at P and Q to the circle x^2 + y^2 = 25 .

Find the locus of the mid point of the chord of the circle x^2+y^2=a^2 which subtend a right angle at the point (0,0).

Prove that the locus of the point of intersection of the tangents at the ends of the normal chords of the hyperbola x^2-y^2=a^2 is a^2(y^2-x^2)=4x^2y^2dot

Find the locus of the point of intersection of tangents to the ellipse if the difference of the eccentric angle of the points is (2pi)/3dot

From an arbitrary point P on the circle x^2+y^2=9 , tangents are drawn to the circle x^2+y^2=1 , which meet x^2+y^2=9 at A and B . The locus of the point of intersection of tangents at A and B to the circle x^2+y^2=9 is (a) x^2+y^2=((27)/7)^2 (b) x^2-y^2((27)/7)^2 (c) y^2-x^2=((27)/7)^2 (d) none of these

Find the locus of the midpoint of the chord of the circle x^2+y^2-2x-2y=0 , which makes an angle of 120^0 at the center.