The tangent at (1,3) to the curve `y=x^(2)+x+1` is also passing though point

The tangent to the curve y=x^(2)+3x will pass through the point (0,-9) if it is drawn at the point

The slope of the tangent to the curve y=x^(3)+x+54 which also passes through the originis

The tangent to the curve y=xe^(x^2) passing through the point (1,e) also passes through the point

Find the equation of the tangent and the normal to the curve y = x^(2) + 4x + 1 at the point where x = 3

Find the equation of tangent and normal to the curve y =3x^(2) -x +1 at the point (1,3) on it.

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.

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

The tangent at the point (2,-2) to the curve,x^(2)y^(2)-2x=4(1-y) does not pass through the point:

The tangents to the curve y=(x-2)^(2)-1 at its points of intersection with the line x-y=3, intersect at the point: