The coordinates of points P(xy) 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


Correct option is

(2, 3)

Any point on the ellipse is given by 


Hence the equation of the tangent at  is


Therefore, the tangent cuts the coordinate axes at the points


Thus the area of the triangle formed by this tangent and the coordinate axes is



But cosec 2θ is smallest when θ = π/4. Therefore A is smallest when θ = π/4.

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


The equation of the common tangent to the curves y2 = 8x and xy = –1 is 



If ab > 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