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Classify the graph of the equation \(x^2+y^2-8x+4y=29\).
circle
exponential curve
line
parabola
Write an equation that states \((x,y)\) is the same distance from \((4,1)\) as it is from the \(x\)-axis.
Select all equations that describe the parabola with its focus \((\text- 1,\text- 7)\) and with \(y=3\) as its directrix.
\((x-1)^2+(y-7)^2=(y+3)^2\)
\((x+1)^2+(y+7)^2=(y-3)^2\)
\(y=\text{-}20(x+1)^2-2\)
\(y=\text{-}20(x+1)^2+2\)
\(y=\text{-}\frac{1}{20}(x+1)^2-2\)
\(y=\text{-}\frac{1}{20}(x+1)^2+2\)
Parabola A and parabola B both have the \(x\)-axis as the directrix. Parabola A has its focus at \((3,2)\) and parabola B has its focus at \((5,4)\). Select all true statements.
Parabola A is wider than parabola B.
Parabola B is wider than parabola A.
The parabolas have the same line of symmetry.
The line of symmetry of parabola A is to the right of that of parabola B.
The line of symmetry of parabola B is to the right of that of parabola A.
A parabola has its focus as \((5,1)\), and \(y = \text{-}3\) as its directrix. Where is the parabola’s vertex?