Find the point on the curve `y^2=4x` which is nearest to the point (2,1).

The point on the curve x^2=2y which is nearest to the point (0,5) is --

Consider the curve 2y=3-x^2 Find the points on the curve at which tangent is parallel to the line x+y=0.

Consider the curve y=x^3+8x+3 .Find the point on the curve at which the slope of the tangent is 20.

Find the equation of the normal to the curve x^2 =9y which passes through the point (6,4).

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

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.

Find the equation of the tangent to the curve y=x^2-4x+5 which is parallel to the line 2x+y+5=0.

Consider the function y^2=4x+5 Find a point on the curve at which the tangent is parallel to the line y=2x+7 .

If the point (a,b) on the curve y= sqrt(x) is close to the point (1,0) , then the value of ab is a) 1/2 b) (sqrt2)/(2) c) 1/4 d) (sqrt2)/(4)