Unit 13 Mastery Check

Write the circle centered at $(4,-1)$ through $(1,3)$.

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Write the circle centered at $(4,-1)$ through $(1,3)$.

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State the defining idea behind conics as loci and the circle foundation in one precise sentence.

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For conics as loci and the circle foundation, what condition or domain restriction must remain visible in the solution?

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For $(y+2)^2=-8(x-1),$ find vertex, focus, and directrix.

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For $(y+2)^2=-8(x-1),$ find vertex, focus, and directrix.

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State the defining idea behind parabolas from focus and directrix in one precise sentence.

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For parabolas from focus and directrix, what condition or domain restriction must remain visible in the solution?

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Find foci of$$\frac{x^2}{36}+\frac{y^2}{20}=1$$

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Find foci of$$\frac{x^2}{36}+\frac{y^2}{20}=1$$

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State the defining idea behind ellipses in one precise sentence.

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For ellipses, what condition or domain restriction must remain visible in the solution?

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Find vertices and asymptotes of$$\frac{y^2}{25}-\frac{x^2}{9}=1$$

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Find vertices and asymptotes of$$\frac{y^2}{25}-\frac{x^2}{9}=1$$

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State the defining idea behind hyperbolas in one precise sentence.

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For hyperbolas, what condition or domain restriction must remain visible in the solution?

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Put $x^2-4x-y^2-6y=12$ in standard form.

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Put $x^2-4x-y^2-6y=12$ in standard form.

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State the defining idea behind completing squares in two variables in one precise sentence.

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For completing squares in two variables, what condition or domain restriction must remain visible in the solution?

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What conic type is suggested by opposite-sign squared terms?

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What conic type is suggested by opposite-sign squared terms?

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State the defining idea behind translated conics and general equations in one precise sentence.

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For translated conics and general equations, what condition or domain restriction must remain visible in the solution?

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Graph$$x^2-y^2=0$$

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Graph$$x^2-y^2=0$$

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State the defining idea behind degenerate conics and classification in one precise sentence.

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For degenerate conics and classification, what condition or domain restriction must remain visible in the solution?

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Classify a conic with eccentricity $1.4$.

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Classify a conic with eccentricity $1.4$.

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State the defining idea behind eccentricity and unified conic structure in one precise sentence.

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For eccentricity and unified conic structure, what condition or domain restriction must remain visible in the solution?

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How does a repeated substitution root usually appear geometrically?

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How does a repeated substitution root usually appear geometrically?

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State the defining idea behind nonlinear systems involving conics in one precise sentence.

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For nonlinear systems involving conics, what condition or domain restriction must remain visible in the solution?

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