- #1
cyberhat
- 2
- 0
Hey guys,
I'm currently a freshman at my local community college. I felt the need to solidify my foundation in Trig so I am currently doing a self-study course.
The question is from I.M Gelfand's book on Trigonometry. Chapter 0, page 9, exercise 8.
8) Two points, A and B, are given in the plane. Describe the set of points for which AX^2-BX^2 is constant.
The chapter focuses on right triangles and Pythagorean theorem. Dunno if this will help but I think exercise 7 was given as a hint to solve exercise 8:
Two points, A and B, are given in the plane. Describe the set of points X such that AX^2+BX^2=AB^2.
The book gave the answer: "A circle with its center at the midpoint AB".
I understood exercise 7 after a couple of minutes, but exercise 8 is making me pull hairs!
My attempt at the solution was to manipulate AX^2-BX^2 and get rid of the negative sign...But even if it could be done, don't know how much help it would give me.
I'm not looking for complete answers -just a small hint. Can't spend 5 hours a day on one problem but don't want to forfeit thinking opportunities either.
P.S I don't know why, but I keep thinking this equation represents a rectangle of sorts.
I'm currently a freshman at my local community college. I felt the need to solidify my foundation in Trig so I am currently doing a self-study course.
The question is from I.M Gelfand's book on Trigonometry. Chapter 0, page 9, exercise 8.
8) Two points, A and B, are given in the plane. Describe the set of points for which AX^2-BX^2 is constant.
The chapter focuses on right triangles and Pythagorean theorem. Dunno if this will help but I think exercise 7 was given as a hint to solve exercise 8:
Two points, A and B, are given in the plane. Describe the set of points X such that AX^2+BX^2=AB^2.
The book gave the answer: "A circle with its center at the midpoint AB".
I understood exercise 7 after a couple of minutes, but exercise 8 is making me pull hairs!
My attempt at the solution was to manipulate AX^2-BX^2 and get rid of the negative sign...But even if it could be done, don't know how much help it would give me.
I'm not looking for complete answers -just a small hint. Can't spend 5 hours a day on one problem but don't want to forfeit thinking opportunities either.
P.S I don't know why, but I keep thinking this equation represents a rectangle of sorts.