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

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 are drawn to the hyperbola 4x^2-y^2=36 at the points P and Q. If these tangents intersect at the point T(0,3) then the area (in sq units) of triangle PTQ is

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

From the point (2, 2) tangent are drawn to the hyperbola (x^2)/(16)-(y^2)/9=1. Then the point of contact lies in the (a)first quadrant (b) second quadrant (c)third quadrant (d) fourth quadrant

Find the equation of tangents drawn to the parabola y=x^2-3x+2 from the point (1,-1)dot

Find the range of parameter a for which a unique circle will pass through the points of intersection of the hyperbola x^2-y^2=a^2 and the parabola y=x^2dot Also, find the equation of the circle.

Find the range of parameter a for which a unique circle will pass through the points of intersection of the hyperbola x^2-y^2=a^2 and the parabola y=x^2dot Also, find the equation of the circle.

How many real tangents can be drawn from the point (4, 3) to the hyperbola (x^2)/(16)-(y^2)/9=1? Find the equation of these tangents and the angle between them.

Statement 1 : If from any point P(x_1, y_1) on the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=-1 , tangents are drawn to the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1, then the corresponding chord of contact lies on an other branch of the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=-1 Statement 2 : From any point outside the hyperbola, two tangents can be drawn to the hyperbola.

Tangents are drawn from any point on the hyperbola (x^2)/9-(y^2)/4=1 to the circle x^2+y^2=9 . Find the locus of the midpoint of the chord of contact.