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Consider the graphs y \equal{} Ax^2 and and y^2 \plus{} 3 \equal{} x^2 \plus{} 4y, where

A

is a positive constant and

x

and

y

are real variables. In how many points do the two graphs intersect?

<span class='latex-bold'>(A)</span>\ \text{exactly } 4 \qquad <span class='latex-bold'>(B)</span>\ \text{exactly } 2

<span class='latex-bold'>(C)</span>\ \text{at least } 1, \text{ but the number varies for different positive values of } A

<span class='latex-bold'>(D)</span>\ 0 \text{ for at least one positive value of } A \qquad <span class='latex-bold'>(E)</span>\ \text{none of these}

Problem Statement