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Algebra
Question

Sketch the locus of the point \( P ( x , y ) \) th...

Sketch the locus of the point \( P ( x , y ) \) that is subject to each of the following conditions. Then use the graph to write down its equation. (a) \( P \) is \( 2 \) units below the \( x \) -axis. (b) \( P \) is \( 1 \) unit to the left of the \( y \) -axis. (c) \( P \) is equidistant from the lines \( y = - 1 \) and \( y = 5 \) . (d) \( P \) is \( 3 \) units from the origin. (e) \( P \) is \( 3 \) units from the point \( ( - 3,1 ) \) . (f) \( P \) is equidistant from the lines with equations \( y = x + 3 \) and \( y = x + 7 \) . (g) The distance of \( P \) from the \( x \) -axis is three times its distance from the \( y \) -axis. 

Answer

(a) \( y = - 2 \) (b) \( x = - 1 \) (c) \( y = 2 \) (d) \( x ^ { 2 } + y ^ { 2 } = 9\) 

(e) \( ( x + 3 ) ^ { 2 } + ( y - 1 ) ^ { 2 } = 9 \) (f) \( y = x + 5\) 

(g) \( y = 3 x \) or \( y = - 3 x\) 

Solution
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