The line `y = x - 2` cuts the parabola `y^2 = 8x` in the points A and B. The normals drawn to the parabola at A and B intersect at G. A line passing through G intersects the parabola at right angles at the point C, and the tangents at A and B intersect at point T.

The sraight line 3x-4y+c=0 Intersects the parabola x^(2)=4y at the points A and B Ifthe tangents to the parabola at A and B are perpendicular,then c=

The straight lines y=+-x intersect the parabola y^(2)=8x in points P and Q, then length of PQ is

The line y=(2x+a) will not intersect the parabola y^(2)=2x if

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 the line 5x-4y-12=0 meets the parabola x^(2)-8y in A and B then the point of intersection of the two tangents at A and B 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 .

If a line x+ y =1 cut the parabola y^2 = 4ax in points A and B and normals drawn at A and B meet at C. The normals to the parabola from C other than above two meets the parabola in D, then point D is : (A) (a,a) (B) (2a,2a) (C) (3a,3a) (D) (4a,4a)