Find the position of the line y=2x+3 with respect to the curve `y=x^(2)+x+1`

Find the position of the points (1, 1) and (2, -1) with respect to the line 3x+4y-6=0 .

Find the point on the curve y=x^3+x^2+x at which the tangent to the curve is perpendicular to the x+y=1

Find the equation of the tangent line to the curve y=x^(2)+4x-16 which is parallel to the line 3x-y+1=0 .

Find the inclination to the positive x-axis of the tangent to the curve 2y = 2-x^2 at the point (1, 1/2)

Find the angle between the lines joining the origin to the points of intersection of the straight line y=3x+2 with the curve x^(2)+2xy+3y^(2)+4x+8y=11=0 .

Find the equation of the tangent line to the curve y=x^(2)-2x+7 which is : (a) parallel to the line 2x-y+9=0 (b) perpendicular to the line 5y-15x=13.

Find the intercept made by the line y=x on the curve y=x^(2)

Find the intercept made by the line y=x on the curve y=x^(3)

Find the equation of the tangent line to the curve y = x^2 - 2x + 9 , which is parallel to the line 2x - y + 7 = 0 .

Find the shortest distance between the line x-y+1=0 and the curve y^(2)=x