Conic Sections Flashcards: Parabola to Hyperbola

Question 1

State the standard form equation of a circle.

Accepted Answer

$$(x-h)^2+(y-k)^2=r^2$$ Center is $(h,k)$ and radius is $r>0$.

Question 2

For $\frac{(x-2)^2}{25}+\frac{(y+1)^2}{9}=1$, find the foci.

Accepted Answer

$c^2=a^2-b^2=25-9=16\Rightarrow c=4$. Center $(2,-1)$. Foci $(2\pm4,-1)$, i.e., $(-2,-1)$ and $(6,-1)$.

Question 3

What is the difference between standard form and general form for conics?

Accepted Answer

Standard form has completed squares and reveals graph features directly (center/vertex, $a,b,r$, foci, asymptotes). General form is $Ax^2+Bxy+Cy^2+Dx+Ey+F=0$ (often requires completing the square/rotation to identify the conic).

Conic Sections Flashcards: Parabola to Hyperbola

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