Find the lines that are tangent and normal to the curve at

Question

The given point is on the curve. Find the lines that are (a) tangent and (b) normal to the curve at given point for the following:

1.) x² + xy - y² = -1, (1,2)

2.) (2x²) + 2xy + (8y²) + 11y - 2 = 0, (-1,0)

Find the lines that are tangent and normal to the curve at given point for the following below:

3.) (x²)(y²) = 36 (1,-6)

4.) y = 7 sin (πx-y), (1,0)