In the picture here, 'ABCD' 'is a square. Prove that for any point on the diagonal 'BD', the sum of the 'x' and ' y' coordinates is zero.

A point is on the x-axis. What are its y-coordinates and z coordinates?

A point is on the x-axis. What are its y -coordinate and z-coordinates?

Mark the points where the y coordinates become.the double of 'x' - coordinate.

In the figure,ABCD is a square.Its diagonals are parallelto the coordinate axes.AC=6 and the coordinates ofA is(3, 2) write the coordinates of the vertices C, B and D.

Find the equation of a curve passing through the point (0,1). If the slope of the tangent to the curve at any point (x,y) is equal to the sum of the x coordinate (abscissa) and the product of the x coordinate and y coordinate of that point.

Find the equation of a curve passing through the point (0,-2) given that at any point (x,y) on the curve, the product of the slope of its tangent and y coordinate of the point is equal to the x coordinate of the point.

C' is the centre of the circle passing through the origin. Circle cúts the 'y' axis at 'A(0,4)' and the axis at 'B(4,0)'. a) Write coordinates of C. b) Write the equation of the circle. c) '(0,0)' is a point on the circle. There is one more point on the circle with. 'x' and y coordinates'equal. Which is that point?

Find the equation of a curve passing through the origin given that the slope of the tangent to the curve at any point (x,y) is equal to the sum of the coordinate of the point.

Find the equation of a curve passing through the point (2,-2) given that at any point (x, y) on the curve the product of the slope of its tangent and y coordinate of the point is equal to the x - coordinate of the point.

Prove that for all points on the line joining the origin and the point (4,2), the 'x' -coordinate is dơuble the 'y-' coordinate. What is the equation of this line?