The parabola `x = y^2 + ay+b` intersect the parabola `x^2=y` at (1,1) at right .which of the foolowing is /are correct?

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

Consider the parabola whose equation is y=x^(2)-4x and the line y=2x-b. Then whichfollowing is/are correct?

The tangent at the point P(x_(1),y_(1)) to the parabola y^(2)=4ax meets the parabola y^(2)=4a(x+b) at Q and R .the coordinates of the mid-point of QR are

if the tangent to the parabola y=x(2-x) at the point (1,1) intersects the parabola at P. find the co-ordinate of P.

If a tangent to the parabola y^(2)=4ax intersects the (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 at A and B, then the locus of the point of intersection of tangents at A and B to the ellipse is

If the tangents to the parabola y^(2)=4ax intersect the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 at A and B, then find the locus of the point of intersection of the tangents at A and B.

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.