Prove that the area of the traingle inscribed in the parabola `y^2=4ax` is `1/(8a)(y_1~y_2)(y_2~y_3)(y_3~y_1)`, where `y_1,y_2,y_3` are the ordinates of the vertices.

If the tangents to the parabola y^(2)=4ax at (x_(1),y_(1)),(x_(2),y_(2)) intersect at (x_(3),y_(3)) then

If the tangents to the parabola y^(2)=4ax at (x_1,y_1) and (x_2,y_2) meet on the axis then x_1y_1+x_2y_2=

If the tangents to the parabola y^2=4ax at the points (x_1,y_1) and ( (x_2,y_2) meet at the point (x_3,y_3) then

If y_(1),y_(2),y_(3) be the ordinates of a vertices of the triangle inscribed in a parabola y^(2)=4ax then show that the area of the triangle is (1)/(8a)|(y_(1)-y_(2))(y_(2)-y_(3))(y_(3)-y_(1))|

If y_(1),y_(2),andy_(3) are the ordinates of the vertices of a triangle inscribed in the parabola y^(2)=4ax , then its area is

Show that the equation of the chord of the parabola y^2 = 4ax through the points (x_1, y_1) and (x_2, y_2) on it is : (y-y_1) (y-y_2) = y^2 - 4ax

If (x_1,y_1),(x_2,y_2)" and "(x_3,y_3) are the feet of the three normals drawn from a point to the parabola y^2=4ax , then (x_1-x_2)/(y_3)+(x_2-x_3)/(y_1)+(x_3-x_1)/(y_2) is equal to

If a parabola y^(2)=4ax followed by x_(1)x_(2)=a^(2),y_(1)y_(2)=-4a^(2) then (x_(1),y_(1)),(x_(2),y_(2)) are

The coordinates of the ends of a focal chord of the parabola y^(2)=4ax are (x_(1),y_(1)) and (x_(2),y_(2)). Then find the value of x_(1)x_(2)+y_(1)y_(2)

Equilateral traingles are circumscribed to the parabola y^2=4ax . Prove that their angular points lie on the conic (3x+a)(x+3a)=y^2