A parabola `y=x^(2)-15x+36` cuts the x -axis at P and Q. A circle is drawn through P and Q so that the origin is outside it.The length of tangent to the circle from (0,0) is

A parabola y=ax^(2)+bx+c(ac>0) crosses the x-axis at A and B .A variable circle is drawn passing through A and B .The length of a tangent from the origin to the circle is

A circle is drawn through the point of intersection of the parabola y=x^(2)-5x+4 and the x-axis such that origin lies outside it. The length of a tangent to the circle from the origin is ________ .

A straight line x+2y=1 cuts the x and y axis at A and B.A circle passes through point A and B and origin.Then the sum of length of perpendicular from A and B on tangent of the circle at the origin is

A parabola y=a x^2+b x+c crosses the x-axis at (alpha,0) and (beta,0) both to the right of the origin. A circle also pass through these two points. The length of a tangent from the origin to the circle is sqrt((b c)/a) (b) a c^2 (c) b/a (d) sqrt(c/a)

The angle between the tangents to the circle with centre (4,5) drawn from P(-2,-3) is 120^(0) then length of the tangent to the circle from P is

For the parabola y^(2)=8x tangent and normal are drawn at P(2.4) which meet the axis of the parabola in A and B .Then the length of the diameter of the circle through A,P,B is

P(a,5a) and Q(4a,a) are two points. Two circles are drawn through these points touching the axis of y. Centre of these circles are at

A tangent is drawn to the parabola y^(2)=4ax at P such that it cuts the y-axis at Q. A line perpendicular to this tangents is drawn through Q which cuts the axis of the parabola at R. If the rectangle PQRS is completed, then find the locus of S.