Suppose that three points on the parabola `y=x^2` have the property that their normal lines intersect at a common point (a, b). The sum of their x-coordinates is

Tangents PT and QT to the parabola y^2 = 4x intersect at T and the normal drawn at the point P and Q intersect at the point R(9, 6) on the parabola. Find the coordinates of the point T . Show that the equation to the circle circumscribing the quadrilateral PTQR , is (x-2) (x-9) + (y+3) (y-6) = 0 .

The lines y=mx+b and y=bx+m intersect at the point (m-b,9) .The sum of the x intercepts of the lines is

The line x+y=6 is normal to the parabola y^(2)=8x at the point.

The line x+y=6 is normal to the parabola y^(2)=8x at the point.

Find the points of intersection of the parabola y^2=8x and the line y=2x.

The angle between tangents to the parabola y^(2)=4x at the points where it intersects with the line x-y -1 =0 is

In parabola y^2=4x, From the point (15,12), three normals are drawn to the three co-normals point is

Locus of the point of intersection of normals to the parabola y^(2)=4 a x at the end points of its focal chord is