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Algebra
Question

The variable point \(P ( x , y )\) moves so that ...

The variable point \(P ( x , y )\) moves so that it is equidistant from the point \(S ( 3,3 )\) and the line \(y + 1 = 0\) . Let \(L\) be the point \(( x , - 1 )\) .

(a) Show that \(P S ^ { 2 } = ( x - 3 ) ^ { 2 } + ( y - 3 ) ^ { 2 }\) and \(P L ^ { 2 } = ( y + 1 ) ^ { 2 }\) .

(b) By setting \(P S ^ { 2 } = P L ^ { 2 }\) , derive the equation of the locus of \(P\) .

Answer

\(\text { (b) } ( x - 3 ) ^ { 2 } = 8 ( y - 1 )\)

Solution
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