1. I assume that the equation of the curve reads:
The curve is an ellipse which contains the point A(1, -1).
2. Use implicite deifferentiation to get the gradient at A:
. Plug in the values for x and y and solve the equation for y': I've got
The direction perpendicular to y' has the slope m = -11. Use the point-slope-formula to calculate the equation of the line:
I've attached a sketch of the situation.