Solution Found!
Another construction for a hyperbola Suppose two circles
Chapter 9, Problem 75E(choose chapter or problem)
Suppose two circles are centered at \(F_1\) and \(F_2\), respectively, whose centers are at least 2a units apart (see figure). The radius of one circle is 2a + r and the radius of the other circle is r, where \(r\ \geq\ 0\). Show that as r increases, the intersection point P of the two circles describes one branch of a hyperbola with foci at \(F_1\) and \(F_2\).
Questions & Answers
QUESTION:
Suppose two circles are centered at \(F_1\) and \(F_2\), respectively, whose centers are at least 2a units apart (see figure). The radius of one circle is 2a + r and the radius of the other circle is r, where \(r\ \geq\ 0\). Show that as r increases, the intersection point P of the two circles describes one branch of a hyperbola with foci at \(F_1\) and \(F_2\).
ANSWER:
Solution 75E
Step 1:
Given that
Suppose two circles are centered at F1 and F2, respectively, whose centers are at least 2a units apart (see figure). The radius of one circle is 2a + r and the radius of the other circle is r, where r ≥ 0.
