Find the point on the curve where tangents to the curve `y^2-2x^3-4y+8=0` pass through (1,2).

Find the equations of the tangents drawn to the curve y^2-2x^3-4y+8=0.

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

Find the slope of the tangent to the curve y = x^(3) – x at x = 2.

Find the length of the tangent for the curve y=x^3+3x^2+4x-1 at point x=0.

Find the point at which the tangent to the curve y=sqrt(4x-3)-1 has its slope (2)/(3) .

Find the equation of the normal to the curve x^(2) = 4y which passes through the point (1, 2).

Find the point on the curve 3x^2-4y^2=72 which is nearest to the line 3x+2y+1=0.

Find the tangent and normal to the following curves at the givne points on the curve. y=x^(2)-x^(4) at (1, 0)

The normal lines to a given curve at each point (x,y) on the curve pass through the point (2,0) the curve passes through the point (2,3) formulate the differential equation representign the problem and hecne find the equation of the curve

The slope of the tangent to the curve (y-x^5)^2=x(1+x^2)^2 at the point (1,3) is.