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

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

Find the equation of the normal lines to the curve 3x^(2)-y^(2)=8 which are parallel to the line x+3y=4 .

The equation of normal to the curve 3x^(2)-y^(2)=8 which is parallel to the line x+3y=8 is ………..

Find the equation of the tangent to the curve y=sqrt(3x-2) which is parallel to the line 4x-2y+5=0 .

Find the points on the curve x^(2)+y^(2)-2x-3=0 at which the tangents are parallel to the X-axis.

Find the equation of the tangent to the curve y^(2)=16x which is parallel to the line 4x-y=1 .

Find the equations of the tangent to the curve y=cos(x+y) which is parallel to the line x+2y=0 .

Find the points on the curve y=x^3-2x^2-x at which the tangent lines are parallel to the line y=3x-2

Find the equation of the normals to the curve y=x^(3)+2x+6 which are parallel to the line x+14y+4=0 .