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Which of the following curves goes through the point (2, 3) and has the property that, for any tangent drawn to it, the portion of the tangent intercepted between the coordinate axes is divided into two equal parts by the point of tangency?
- 2y - 3x = 0
- y = 6/x
- x² + y² = 13
- (x/2)² + (y/3)² = 2
Correct answer: y = 6/x
Solution
The curve y = 6/x has the property that any tangent line drawn to it will intercept the axes in such a way that the segments created are equal in length, which is a characteristic of rectangular hyperbolas. Additionally, it passes through the point (2, 3), confirming it as the correct option.
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