(from the 1994 Putnam Exam) Find the value of m so that the line y = mx bisects the

Chapter 5, Problem 9

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QUESTION:

(from the 1994 Putnam Exam) Find the value of m so that the line y = mx bisects the region _ (x, y) R2 : x2 4 + y2 1, x 0, y 0 _ . (Hint: How are ellipses, circles, and linear transformations related?)

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QUESTION:

(from the 1994 Putnam Exam) Find the value of m so that the line y = mx bisects the region _ (x, y) R2 : x2 4 + y2 1, x 0, y 0 _ . (Hint: How are ellipses, circles, and linear transformations related?)

ANSWER:

Step 1 of 3

Stretch the ellipse  by a factor 2 along the y-axis. The point  on the curve become .

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