Consider the circle `x^2+y^2-2x-4y=0`. If O represents origin , point P is `(1+sqrt5,2)` and R is the intersection of the tangent drawn at P and O , then find area of `triangle OPR`

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

Consider the graph of y=x^2. Let A be a point on the graph in the first quadrant. Let B be the intersection point of the tangent on y=x^2 at the point A and the x-axis. If the area of the figure surrounded by the graph of y=x^2 and the segment OA is (p/q) times as large as the area of the triangle OAB (where O is origin), then find the least value of (p+q) where p, q in N.

The circle x^(2)+y^(2)-2x-6y+2=0 intersects the parabola y^(2)=8x orthogonally at the point P. The equation of the tangent to the parabola at P can be

A line y=2x+c intersects the circle x^(2)+y^(2)-2x-4y+1=0 at P and Q. If the tangents at P and Q to the circle intersect at a right angle,then |c| is equal to

If tangents PA and PB are drawn to circle (x+3)^(2)+(y-2)^(2)=1 from a variable point P on y^(2)=4x, then the equation of the tangent of slope 1 to the locus of the circumcentre of triangle PAB IS

The line 4x -7y + 10 = 0 intersects the parabola y^(2) =4x at the points P and Q. The coordinates of the point of intersection of the tangents drawn at the points P and Q are

If normal of circle x^(2)+y^(2)+6x+8y+9=0 intersect the parabola y^(2)=4x at P and Q then find the locus of point of intersection of tangent's at P and Q.

Tangents are drawn to the circle x^2+y^2=50 from a point 'P' lying on the x-axis. These tangents meet the y-axis at points P_1' and P_2' . Possible coordinates of 'P' so that area of triangle PP_1P_2 is minimum , is/are