At what point of the parabola `y^2 = 18x`, does the ordinate increase at twice the rate of the abscissa?

For the parabola y^2=20x write down the co-ordinates of the focus,length of the latus rectum.

Find the point on the curve y^2 = 8x at which the abcissa and the ordinate change at the same rate.

At what point does the line 3x+2y+3=0 cuts the y-axis?

Using LMV theorem find a point on the parabola y = (x-3)^2 . Where tangents is parallel to the chord joining (3, 0), (5, 4).

Find the points on the curve y^2 = x^2 (a - x) where the tangent is perpendicular to the X-axis

The length x of a rectangle is decreasing at the rate of 5 cm/min and the width y is increasing at the rate of 4 cm/min. When x = 8 cm and y = 6 cm, find the rates of change of the perimeter

The length x of a rectangle is decreasing at the rate of 5 cm/min and the width y is increasing at the rate of 4 cm/min. When x = 8 cm and y = 6 cm, find the rates of change of the area of the rectangle