If `y_1, y_2, y_3` be the ordinates of a vertices of the triangle inscribed in a parabola `y^3=4a x ,` then show that the area of the triangle is `1/(8a)|(y_1-y_2)(y_2-y_3)(y_3-y_1)|dot`

If y_1, y_2, y_3 be the ordinates of a vertices of the triangle inscribed in a parabola y^2=4a x , then show that the area of the triangle is 1/(8a)|(y_1-y_2)(y_2-y_3)(y_3-y_1)|dot

If y_1, y_2, y_3 be the ordinates of a vertices of the triangle inscribed in a parabola y^2=4a x , then show that the area of the triangle is 1/(8a)|(y_1-y_2)(y_2-y_3)(y_3-y_1)|dot

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

The area of the triangle inscribed in the parabola y^(2)=4x the ordinates of whose vertices are 1, 2 and 4 square units, is

The coordinates of the vertices of a triangle are (4, -3), (-5, 2) and (x, y). If the centroid of the triangle is at the origin, show that x=y=1 .

Find the vertices and the area of the triangle whose sides are x=y, y=2x and y=3x+4 .

The coordinates of the ends of a focal chord of the parabola y^2=4a x are (x_1, y_1) and (x_2, y_2) . Then find the value of x_1x_2+y_1y_2 .

Prove that the area of the triangle inscrbed in the paravbola y^(2)=4ax is (1)/(8a)|(y_(1)-y_(2))(y_(2)-y_(3))(y_(3)-y_(1))| sq. units where y_(1),y_(2),y_(3) are the ordinates of its vertices.

The area of the figure bounded by the parabola (y-2)^(2)=x-1, the tangent to it at the point with the ordinate y=3, and the x-axis is

Find the area of the triangle formed by the line x+y=3 and the angle bisectors of the pair of lines x^2-y^2+2y=1