Algebra 2
Quadratic functions (advanced)
Parabolas from focus, directrix, axis of symmetry
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Questions
Question 1
179416
A parabola is defined as the set of all points \((x, y)\) equidistant from a fixed point (the \(\textbf{focus}\)) and a fixed line (the \(\textbf{directrix}\)). Consider the parabola with focus \(F = (0, 2)\) and directrix \(y = -2\).
(i) Write an equation stating that the distance from \((x, y)\) to \(F\) equals the distance from \((x, y)\) to the directrix.(ii) Square both sides and simplify to obtain the equation of the parabola.
(iii) State the coordinates of the vertex.
Part a:
\(x^2 = 8y\)
Correct
\(x^2 = -8y\)
\(y^2 = 8x\)
\(x^2 = 4y\)
Part b:
\((0, 2)\)
\((0, 0)\)
Correct
\((2, 0)\)
\((0, -2)\)
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