I have problems solving this, seems a bit more complicated than other similar problems.
For which parameter a (real number) is y=(3/2)*x-2 tangent of curve (y^2)*x+a=x^2+y^2?
there is probably a more accurate way to do this question - but here is what I've done:
2. By partial differentiation you'll get:
4. Solve this equation for x:
5. From the equation of the line you'll get:
6. Set equal those terms in x:
and solve for y.
7. You'll get 2 values for y: y = 1 or
8. The corresponding x-values are x = 2 or
9. Plug in these values for x and y into the equation of the curve to determine a:
Graph in brown, tangent point in red.
Graph in blue, tangent point in violet.