perplexus.info :: Just Math : 4 distinct pairs

4 distinct pairs (Posted on 2023-02-20)

For what values of a
will the set of equations:
x² + y² = 4 + 2ax - a²
x² = y²

have 4 distinct solutions?

No Solution Yet Submitted by Ady TZIDON

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re: Solution

| Comment 4 of 5 |

(In reply to Solution by Brian Smith)

If a = 2 or a = -2, I think there are only 3 solutions for (x,y)

(0,0), (2,2), (2,-2).

The equation where I plugged in x^2 for y^2 becomes:

2x^2 ± 4x = 0

x can be 0 or ±2, but for the 0 value there is only one y value, 0.

Posted by Larry on 2023-02-20 10:50:52

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