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In the general form of a conic with no xy term, A equals 5 and C equals 5. Which curve is it?
AA circle
BAn ellipse
CA parabola
DA hyperbola
Answer & Solution
Correct answer: A. A circle
1. Write the equation as Ax squared plus Cy squared plus Dx plus Ey plus F equals 0.
2. Both A and C are nonzero and both equal 5, so they match in size and in sign.
3. Equal nonzero coefficients of the same sign make the graph a circle.
4. An ellipse needs A and C to share a sign but differ in size, which fails here.
_Source: OpenStax College Algebra (CC BY 4.0), Ch 8 "Analytic Geometry", section 8.4 Rotation of Axes_
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