The Equation Of The Common Tangent To The Curves y2 = 8x and xy = –1 Is   

A dynamite blast blows a heavy rock starting up with a launch velocity to 160 m/sec. It reaches a height of s = 160t – 16t² after t sec. The velocity of the rock when it is 256 m above ground on the way up is

The slope of the tangent to the curve represented by x = t² + 3t – 8 and y = 2t² – 2t – 5 at the point M (2, –1) is

The coordinates of the point P on the curve y² = 2x³, the tangent at which is perpendicular to the line 4x – 3y + 2 = 0, are given by

The coordinates of points P(x, y) lying in the first quadrant on the ellipsex²/8 + y²/18 = 1 so that the area of the triangle formed by the tangent at Pand the coordinate axes is the smallest, are given by

The points(s) on the curve y³ + 3x² = 12y where the tangent is vertical is(are)

If a, b > 0 then the minimum value of  

The curve y = ax³ + bx² + cx + 8 touches x – axis at P(–2, 0) and cuts they – axis at a point Q where its gradient is 3. The value of a, b, c are respectively

If the tangent at (1, 1) on y² = x(2 – x)² meets the curve again at P, is

The tangent to the curve 

At the point corresponding to  is

The points of contact of the vertical tangents to x = 2 – 3 sinθ,  y = 3 + 2 cos θ are