Ten multiple-choice questions check the definition of a parabola, equations from a focus and a directrix, and the main facts about tangent lines to circles and their constructions. Each question has exactly one correct answer.
Which statement defines a parabola?
A parabola has focus \((0,3)\) and directrix \(y=-3\). Which equation describes it?
What is the focus of the parabola \(x^{2}=16y\)?
What is the focus of the parabola \(y^{2}=-8x\)?
The parabola shown has vertex V(1, 2) and focus F(1, 4). What is the equation of its directrix?
In the figure, \(\overline{PT}\) is tangent to the circle at T, \(OT=6\) and \(PT=8\). Find OP.
Tangent segments \(\overline{PA}\) and \(\overline{PB}\) have lengths \(5x-3\) and \(2x+9\). What is PA?
In the construction of a tangent from P to the circle with center O, M is the midpoint of OP. What is the next step?
Tangents from P touch a circle with center O at A and B, and \(m\angle APB=62^{\circ}\). Find \(m\angle AOB\).
Segment PT is drawn from P to a point T on a circle with center O. Which lengths (OT, PT, OP) show that PT is tangent at T?
🎉 Quiz complete!
Remember:
- A parabola is the set of points equidistant from the focus and the directrix (G-GPE.A.2).
- Vertex (h, k): (x – h)^2 = 4p(y – k) has focus (h, k + p) and directrix y = k – p; (y – k)^2 = 4p(x – h) opens sideways.
- p is the signed distance from the vertex to the focus; a negative p means the parabola opens down or left.
- A tangent to a circle is perpendicular to the radius at the point of tangency (G-C.A.4).
- Tangent segments from one outside point are congruent; the circle on diameter OP gives the tangent points in a construction.
See every chapter on the Geometry math page.