Precalculus Conic Sections Quiz: 10 Questions with Explanations

A 49B 3.5C 7D 1

r squared = 49, so r = 7.

A \((0,5)\)B \((0,20)\)C \((5,0)\)D \((0,10)\)

4p = 20, so p = 5, and the focus is p units above the vertex.

A \(\frac{x^{2}}{9}-\frac{y^{2}}{4}=1\)B \(\frac{x^{2}}{9}+\frac{y^{2}}{4}=1\)C \(x^{2}+y^{2}=9\)D \(y=x^{2}\)

An ellipse has a plus sign and different denominators.

A \((\pm5,0)\)B \((\pm3,0)\)C \((0,\pm4)\)D \((\pm4,0)\)

c = sqrt(25 – 9) = 4 on the horizontal major axis.

A \(y=\pm\frac52x\)B \(y=\pm\frac25x\)C \(y=\pm5x\)D \(y=\pm\frac{25}{4}x\)

y = plus or minus (b/a)x with b = 5 and a = 2.

A 7B 5C 1D \(\sqrt7\)

c^2 = a^2 + b^2 = 25, so c = 5. For an ellipse you would subtract.

A \(x=2\)B \(y=-2\)C \(x=-2\)D \(x=-8\)

4p = 8, p = 2. The parabola opens right, so the directrix is x = -p = -2.

A \((5,-3)\)B \((-5,3)\)C \((10,-6)\)D \((5,3)\)

x^2 – 10x + 25 and y^2 + 6y + 9 give (x – 5)^2 + (y + 3)^2 = 25.

A At the vertexB At the focusC On the directrixD At the rim

Signals parallel to the axis reflect to the focus.

A EllipseB CircleC ParabolaD Hyperbola

A hyperbola consists of two separate branches.