For which value of k does the pair of equations x2 y2 0 and x k 2 y2 1 yield a unique positive solut...........

Quantitative Aptitude (CDS) Algebra

For which value of k does the pair of equations x² - y² = 0 and (x - k)² + y² = 1 yield a unique positive solution of x?

$\sqrt{2}$

$- \sqrt{2}$

From 1st equation we know that (x)²=y²

Substituting this in 2nd equation. we get , 2∗x²−2∗x∗k+k²−1=0
2∗x²−2∗x∗k+k2−1=0 and for unique solution b²−4ac=0
b²−4ac=0 must satisfy.

This is possible only when k = $\sqrt{2}$

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