1967 AHSME Problems/Problem 14

Problem

The number of distinct points common to the curves $x^2+4y^2=1$ and $4x^2+y^2=4$ is:

$\text{(A) } 0 \quad \text{(B) } 1 \quad \text{(C) } 2 \quad \text{(D) } 3 \quad \text{(E) } 4$

Let $x^2 = a$ and $y^2 = b.$

then

and

By solving we find--

$a=1$

$b=0$

However $a=x^2$ and $b=y^2$

Therefore $y=0$ , and $x=1,-1$

Thus, the only solutions are $(0,1)$ , and $(0,-1)$

So there are only 2 solutions

$\rightarrow$ $\fbox{C}$

1967 AHSME (Problems • Answer Key • Resources)
Preceded by Problem 13	Followed by Problem 15
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