Prove that the curves `y=6+x-x^2 and y(x-1)=x+2,` passes through the point `(2,4)` and there is a common tangent at this Find the equation of the tangent.

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.

Find the equation of the normal at a point on the curve x^(2)=4y , which passes through the point (1,2). Also find the equation of the corresponding tangent.

Find the equation of the normal at a point on the curve x^(2) = 4y , which passes through the point (1, 2). Also, find the equation of the corresponding tangent.

Prove that the curve y^(2)=4x and x^(2)+y^(2)-6x+1=0 touches each other at thepoint (1,2), find the equation of the common tangents.

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.

Find the equations of the normal at a point on the curve x^2=4y , which passes through the point (1,2). Also find the equation of the corresponding tangent.

Prove that the curve y^2=4x and x^2 +y^2 - 6x +1=0 touches each other at thepoint (1, 2), find the equation of the common tangents.

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

Find the equation of the curve passing through the point (1,0) if the slope of the tangent to the curve at any point (x,y)is(y-1)/(x^(2)+x)