Find the equations of the tangents and normal lines to the `y = x^2 at (0, 0)`

Find the equations of the tangents and normal lines to the y = 2x^2 -3x - 1 at (1,-2)

Find the equations of the tangents and normal lines to the y = x^4 - 6x^3 + 13x^2 -10x+ 5 at (1,3)

Find the equations of the tangent and normal lines to the following curves: y = x^2 at (0,0)

Find the equations of the tangent and normal lines to the following curves: y(x-2)(x-3)-x+7=0 at the point, where it meets x=axis.

Find the equations of the tangent and normal lines to the following curves: y = x^3 at (1,2)

Find the equations of the tangent and normal lines to the following curves: y = (1+sinx)/(cosx) at x = pi/4

Find the equations of the tangent and normal to the hyperbola x^2/a^2 - y^2/b^2 = 1 at the point (x_0,y_0)

Find the equations of the tangent and normal to the curve 16x^2 + 9y^2 = 145 at (x_1, y_1) , where x_1=2 and y_1>0 . Also find the points of intersection where both tangent and normal cut the x-axis.

Find the equations of the tangent and normal to the given curves at the points given y = x^2 at (0,0)