In mathematics, what geometric shape represents the locus of points equidistant from a fixed point and a fixed line in the plane?

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In mathematics, what are the solutions to the quadratic equation $3 x^{2} - 12 x + 9 = 0$ ?
In mathematics, what is the derivative of the rational function $f (x) = \frac{3 x - 1}{x ^{2} + 2}$ at $x = 1$ ?
In mathematics, what is the sum of the first 20 terms of an arithmetic progression with first term $a_{1} = 5$ and common difference $d = 3$ ?
In mathematics, what is the sum of the infinite geometric series $12 + 4 + 4/3 + 4/9 + \dots$ ?
In mathematics, which exact value equals $sin (15 0^{\circ})$ in standard trigonometry?
In mathematics, how many solutions does the equation $2 cos^{2} (x) - 3 cos (x) + 1 = 0$ have in the interval $[0, 2 π)$ ?