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

Find the point on the hyperbola x^2/24 - y^2/18 = 1 which is nearest to the line 3x+2y+1=0 and compute the distance between the point and the line.

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

Find the distance of the point on y=x^4+3x^2+2x which is nearest to the line y=2x-1

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 point on the curve y=x^(2)-5x+4 at which the tangent is parallel to the line 3x + y = 7.

Find the asymptotes of the curve x y-3y-2x=0 .

Find the points on the circle x^2+y^2-2x+4y-20=0 which are the farthest and nearest to the point (-5,6)dot

Find the point on the curve y=x^(3)-6x^(2)+x+3 where the normal is parallel to the line x + y = 1729.

Find the equations of the tangents to the curve y=(x+1)/(x-1) which are parallel to the line x + 2y = 6.