On the same axes, sketch the curves given by the equations ${{x}^{2}}+{{y}^{2}}=9$ and ${x^2 - y^2 =

Question

On the same axes, sketch the curves given by the equations ${{x}^{2}}+{{y}^{2}}=9$ and ${x^2 - y^2 = k}$ where ${k}$ is a positive real number, indicating clearly the axes intercepts and equation of asymptotes, if any. Hence, determine the range of values of ${k}$ such that the two curves intersect at exactly four distinct points. [4]

Accepted Answer

$0<k<9$

2015 SAJC Promo P1 Q9

2015 SAJC Promo P1 Q9

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