SAT Math Practice Question #25695 - SATify | SATify

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SAT Math Practice Question #25695 - SATify | SATify

#25695

algebra

geometry

curves

Calculus

hard

120 sec

Which of the following describes the set of values of $a$ for which the curves $x^{2} + y^{2} = a^{2}$ and $x = y^{2} - a$ in the real $x y$ -plane intersect at exactly $3$ points?

A.

$a = \frac{1}{4}$

B.

$\frac{1}{4} < a < \frac{1}{2}$

C.

$a > \frac{1}{4}$

D.

$a = \frac{1}{2}$

E.

$a > \frac{1}{2}$