Find the coordinates of a point on the parabola `y=x^2+7x+2` which is closest to the straight line `y=3x-3.`

Find the point on the parabolas x^2=2y which is closest to the point (0,\ 5) .

Find the equation of the tangent to the parabola y^2 = 4x + 5 which is parallel to the straight line y= 2x+7

Find the point on the straight line 2x+3y=6 , which is closest to the origin.

Find the coordinates of the point on the curve y^2=3-4x where tangent is parallel to the line 2x+y-2=0 .

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

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

Find the area bounded by the parabola y=x^2+1 and the straight line x+y=3.

Find the area bounded by the parabola y=x^2+1 and the straight line x+y=3.

Find the area bounded by the parabola y=x^2+1 and the straight line x+y=3.

Find the coordinates the those point on the line 3x+ 2y = 5 which are equisdistant from the lines 4x+ 3y - 7 = 0 and 2y - 5 = 0