If a circle cuts a parabola in four points show that sum of ordinates of four points is zero.

A circle and a parabola y^2=4a x intersect at four points. Show that the algebraic sum of the ordinates of the four points is zero. Also show that the line joining one pair of these four points is equally inclined to the axis.

If normal to the parabola y^2-4a x=0 at alpha point intersects the parabola again such that the sum of ordinates of these two points is 3, then show that the semi-latus rectum is equal to -1. 5alphadot

If normal to parabola y^(2)=4ax at point P(at^(2),2at) intersects the parabola again at Q, such that sum of ordinates of the points P and Q is 3, then find the length of latus ectum in terms of t.

Prove that through any point, three normals can be drawn to a parabola and the algebraic sum of the ordinates of the three points is zero.

Give four points to show the importance of vegetative propagation.

Statement 1: If the endpoints of two normal chords A Ba n dC D (normal at Aa n dC) of a parabola y^2=4a x are concyclic, then the tangents at Aa n dC will intersect on the axis of the parabola. Statement 2: If four points on the parabola y^2=4a x are concyclic, then the sum of their ordinates is zero.

The sum of the ordinates of two points on y^2=4ax is equal to the sum of the ordinates of two other points on the same curve. Show that the chord joining the first two points is parallel to the chord joining the other two points.

Show that equation to the curve such that the y-intercept cut off by the tangent at an arbitrary point is proportional to the square of the ordinate of the point of tangency is of the form a/x+b/y=1 .

Point M moves on the circle (x-4)^2+(y-8)^2=20 . Then it brokes away from it and moving along a tangent to the circle, cuts the x-axis at the point (-2,0). The co-ordinates of a point on the circle at which the moving point broke away is

If the normals at two points P and Q of a parabola y^2 = 4ax intersect at a third point R on the curve, then the product of ordinates of P and Q is