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

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 .

Find the equation of the smallest circle passing through the point of intersection of the line x+y=1 and the circle x^(2)+y^(2)=9 .

Find the equations of the tangents drawn from the point A(3, 2) to the circle x^2 + y^2 + 4x + 6y + 8 = 0

The straight line 4x + 3y - 12 = 0 intersects the x -and y-axis A and B respectively. Find the coordinates of the point at which the straight line bar(AB) is divided internally into the ratio 2 : 1.

If line x-2y-1=0 intersects parabola y^(2)=4x at P and Q, then find the point of intersection of normals at P and Q.

If the tangent to the ellipse x^2+2y^2=1 at point P(1/(sqrt(2)),1/2) meets the auxiliary circle at point R and Q , then find the points of intersection of tangents to the circle at Q and Rdot

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

Lines x + y = 1 and 3y = x + 3 intersect the ellipse x^(2) + 9y^(2) = 9 at the points P , Q , R . The area of the triangle PQR is _

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.