How to write a system of equation that satisfies the conditions "a hyperbola and a circle that intersect in three points?"
1 Answer
Nov 12, 2016
Explanation:
The circle needs to touch the hyperbola at one point and cut it at the other two.
Choose a nice simple hyperbola:
#x^2-y^2 = 1#
This will intersect the
Then add a circle with centre
#(x-1)^2+y^2 = 2^2#
These will intersect at
graph{(x^2-y^2-1)((x-1)^2+y^2-3.9)((x+1)^2+y^2-0.01)((x-2)^2+(y-sqrt(3))^2-0.01)((x-2)^2+(y+sqrt(3))^2-0.01) = 0 [-5, 5, -2.5, 2.5]}