A line is tangent to a parabola if it intersects the parabola at not more than one point.

The line x+ y +2=0 is a tangent to a parabola at point A, intersect the directrix at B and tangent at vertex at C respectively. The focus of parabola is S(a, 0) . Then

A line L passing through the focus of the parabola y^2=4(x-1) intersects the parabola at two distinct points. If m is the slope of the line L , then (a) -1 1 (c) m in R (d) none of these

A line L passing through the focus of the parabola y^2=4(x-1) intersects the parabola at two distinct points. If m is the slope of the line L , then -1 1 m in R (d) none of these

If the normals drawn at the end points of a variable chord PQ of the parabola y^2 = 4ax intersect at parabola, then the locus of the point of intersection of the tangent drawn at the points P and Q is

If (-2,5) and (3,7) are the points of intersection of the tangent and normal at a point on a parabola with the axis of the parabola, then the focal distance of that point is

The mirror image of the parabola y^2= 4x in the tangent to the parabola at the point (1, 2) is:

A tangent is drawn to the parabola y^(2)=8x at P(2, 4) to intersect the x-axis at Q, from which another tangent is drawn to the parabola to touch it at R. If the normal at R intersects the parabola again at S, then the coordinates of S are

If the bisector of angle A P B , where P Aa n dP B are the tangents to the parabola y^2=4a x , is equally, inclined to the coordinate axes, then the point P lies on the tangent at vertex of the parabola directrix of the parabola circle with center at the origin and radius a the line of the latus rectum.

If tangent at P and Q to the parabola y^2 = 4ax intersect at R then prove that mid point of R and M lies on the parabola, where M is the mid point of P and Q.

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