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.

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

From a point (sintheta,costheta) , if three normals can be drawn to the parabola y^(2)=4ax then the value of a is

From a point (sintheta,costheta) , if three normals can be drawn to the parabola y^(2)=4ax then find the value of a .

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.

From a the point P(h, k) three normals are drawn to the parabola x^2=8y and m_1m_2" and "m_3 are the slopes of three normals, if the two normals from P are such that they make complementary angles with the axis then the directrix of the locus of point P (conic) is :

Prove that "The Algebraic Sum of deviations from Mean is zero".

From the point (15, 12), three normals are drawn to the parabola y^2=4x . Then centroid and triangle formed by three co-normals points is (A) ((16)/3,0) (B) (4,0) (C) ((26)/3,0) (D) (6,0)

From a point (h,k) three normals are drawn to the parabola y^2=4ax . Tangents are drawn to the parabola at the of the normals to form a triangle. The Centroid of G of triangle is

Prove that the orthocentre of the triangle formed by any three tangents to a parabola lies on the directrix of the parabola

Three normals drawn from a point (h k) to parabola y^2 = 4ax