Question

The hyperbola x^2/25 - y^2/9=1. Find an equation for a circle that intersects the hyperbola at
a. zero points.
b. four points.
c. three points

Answer 1

a) here's a very small circle with the same center as the hyperbola with the radius being less than the transverse axis of the hyperbola: x^2+y^2=.001
b) here's a very large circle with the same center as the hyperbola but the radius isgreater than the transverse axis of the hyperbola: x^2+y^2=500000
c) here's a circle that is tangent to one of the vertices of the hyperbola and intersecting the other branch of the hyperbola: (x-5)^2+y^2 = 100