Tangent `P Aa n dP B` are drawn from the point `P` on the directrix of the parabola `(x-2)^2+(y-3)^2=((5x-12 y+3)^2)/(160)` . Find the least radius of the circumcircle of triangle `P A Bdot`

Find the angle between two tangents drawn from the point ( 1,4) to the parabola y^(2) = 12x

Tangents P Aa n dP B are drawn to x^2+y^2=a^2 from the point P(x_1, y_1)dot Then find the equation of the circumcircle of triangle P A Bdot

Tangents PA and PB are drawn to x^2+y^2=a^2 from the point P(x_1, y_1)dot Then find the equation of the circumcircle of triangle P A Bdot

If tangents P Qa n dP R are drawn from a variable point P to thehyperbola (x^2)/(a^2)-(y^2)/(b^2)=1,(a > b), so that the fourth vertex S of parallelogram P Q S R lies on the circumcircle of triangle P Q R , then the locus of P is x^2+y^2=b^2 (b) x^2+y^2=a^2 x^2+y^2=a^2-b^2 (d) none of these

If tangents P Qa n dP R are drawn from a variable point P to thehyperbola (x^2)/(a^2)-(y^2)/(b^2)=1,(a > b), so that the fourth vertex S of parallelogram P Q S R lies on the circumcircle of triangle P Q R , then the locus of P is (a) x^2+y^2=b^2 (b) x^2+y^2=a^2 (c) x^2+y^2=a^2-b^2 (d) none of these

Tangents PT_1, and PT_2 , are drawn from a point P to the circle x^2 +y^2=a^2 . If the point P lies on the line Px +qy + r = 0 , then the locus of the centre of circumcircle of the triangle PT_1T_2 is

Let tangent PQ and PR are drawn from the point P(-2, 4) to the parabola y^(2)=4x . If S is the focus of the parabola y^(2)=4x , then the value (in units) of RS+SQ is equal to

If P be a point on the parabola y^2=3(2x-3) and M is the foot of perpendicular drawn from the point P on the directrix of the parabola, then find length of each sides of an equilateral triangle SMP(where S is the focus of the parabola).

P is a variable on the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 with AA ' as the major axis. Find the maximum area of triangle A P A '

Find the points of contact Q and R of a tangent from the point P(2,3) on the parabola y^2=4xdot