The slope of a curve at (x,y) is `(x^(2)-2)` and it passes through the point (3,8) . Find the equation of the curve

The slope of a curve at ( x,y) is 2x+1 . If the curve passes through the point (-4,2) , find the equation of the curve .

The slope at any point of a curve y=f(x) is given by (dy)/(dx)=3x^(2) and it passes through (-1,1). The equation of the curve is

The slope of the tangent to a curve y=f(x) at (x,f(x)) is 2x+1. If the curve passes through the point (1,2) then the area of the region bounded by the curve, the x-axis and the line x=1 is (A) 5/6 (B) 6/5 (C) 1/6 (D) 1

The slope of the tangent to a curve at any point (x,y) is (3y+2x+4)/(4x+6y+5) . If the curve passes through (0,-1), find the equation of the curve.

The slope of the tangent at (x , y) to a curve passing through a point (2,1) is (x^2+y^2)/(2x y) , then the equation of the curve is

If the slope of the tangent at (x,y) to a curve passing through the point (2,1) is (x^(2)+y^(2))/(2xy) , then the equation of the curve is-

At any point (x,y) of a curve, the slope of the tangent is twice the slope of the line segment joining the point of contact to the point(-4, -3).Find the equation of the curve given that it passes through (-2, 1).

A curve passes through the point (3,-4) and the slope of the tangent to the curve at any point (x,y) is (-(x)/(y)) . Find the equation of the curve.

If the curve y= a sqrt(x) + bx passes through the point (1, 2) and the area bounded by the curve, the line x=4 and x-axis is 8 square unit, then the values of a and b are-