The abscissa of the point on the curve `sqrt(x y)=a+x` the tangent at which cuts off equal intercepts from the coordinate axes is (b) `a//sqrt(2)` (c) `-asqrt(2)` (d) `asqrt(2)`

Find the abscissa of the point on the curve x^(3)=ay^(2) , the normal at which cuts off equal intecepts from the coordinate axes.

Find the abscissa of the point on the curve xy=(c+x)^(2) , the normal at which cuts off numerically equal intercepts from the axes of coordinates.

The slope of the tangent to the curve y=2sqrt2x

The points on the curve 9y^(2) = x^(3) , where the normal to the curve makes equal intercepts with the axes are

Find the equation of a line that cuts off equal intercepts on the coordinate axes and passes through the point (2,3).

Find the equation of the tangent to the circle x^2+y^2+4x-4y+4=0 which makes equal intercepts on the positive coordinates axes.

Find the points on the curve y = x^(3) at which the slope of the tangent is equal to the y-coordinate of the point.

The coordinates of the point(s) on the graph of the function f(x)=(x^3)/3-(5x^2)/2+7x-4 , where the tangent drawn cuts off intercepts from the coordinate axes which are equal in magnitude but opposite in sign, are (a) (2,8/3) (b) (3,7/2) (c) (1,5/6) (d) none of these

Find the coordinates of the point on the curve y=(x)/(1+x^(2)) where the tangent to the curve has the greatest slope.

If at each point of the curve y=x^3-a x^2+x+1, the tangent is inclined at an acute angle with the positive direction of the x-axis, then (a) a >0 (b) a<-sqrt(3) (c) -sqrt(3)< a < sqrt(3) (d) non eoft h e s e