Hyperbola passes through (1; 9) and (-1; 9). Construct a hyperbolic equation. What points of this hyperbola do the circle pass through, whose diameter is determined by the same points.

Question

I am getting the answers with logic, but I don't know how to correctly find the solution.

Answer 1

circle is x^2 + (y-9)^2 = 1

or

x^2 +y^2 -18y = 82

rectangular hyperbola is xy = +/-9

but only the quadrant 1&2 branches

not when both x and y are negative

and not when x is positive y negative

no points below the x axis

where does the circle intersect the hyperbola? (0, +/-9)