Prove that area at triangle will remain same by shifting origin at any point.

Find the curve for which area of triangle formed by x-axis, tangent drawn at any point on the curve and radius vector of point of tangency is constant, equal to a^2

Area of a triangle =____

Consider the parabola y^2 = 8x. Let Delta_1 be the area of the triangle formed by the end points of its latus rectum and the point P( 1/2 ,2) on the parabola and Delta_2 be the area of the triangle formed by drawing tangents at P and at the end points of latus rectum. Delta_1/Delta_2 is :

Prove that an equilateral triangle can be constructed on any given line segment.

Obtain lnght of latus rectum and equation of direction of the parabola (x + 1)^(2) = 4(y + 2) by shifting origin at point (-1, -2).

Find out the shift in point B, C and D

If a triangle and a parallelogram are on the same base and between the same parallels, then prove that the area of the triangle is equal to half the area of the parallelogram.

Prove that two triangles on the same base and between the same parallels are equal in area.

Prove that the area of the equilateral triangle described on the side of a square is half the area of the equilateral triangles described on its diagonal.

Prove that the area of an equilateral triangle described on one side of a square is equal to half the area of the equilateral triangle described on one of its diagonals.