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Question

Find the points on the y-axis, which are at a distance of 13 units each from the point (5,7).

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Solution

Let the point on y-axis be B(0,b) and the given point be A(5,7). The distance between A and B is 13 units.
Now,
AB=13

{0(5)}2+(b7)2=13 [Using Distance formula: d=(x2x1)2+(y2y1)2]

(0+5)2+(b7)2=132 [on squaring both sides]

25+b2+4914b=169

b214b95=0

b219b+5b95=0

b(b19)+5(b19)=0

(b19)(b+5)=0

b=19 or 5
Hence, the points are (0,19) and (0,5).


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