IFind the coordinates of a point on the x-axis which are at a distance of 10 units from the point (-4,8)
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The required coordinate is (x,0) since it is on the X-axis. Then by the given question,
√[{(x-(-4)}²+(0-8)²]=10
or, (x+4)²+(-8)²=100 [squaring both sides]
or, x²+8x+16+64=100
or, x²+8x+80-100=0
or, x²+8x-20=0
or, x²+10x-2x-20=0
or, x(x+10)-2(x+10)=0
or, (x+10)(x-2)=0
∴, either, x=-10 or, x=2
√[{(x-(-4)}²+(0-8)²]=10
or, (x+4)²+(-8)²=100 [squaring both sides]
or, x²+8x+16+64=100
or, x²+8x+80-100=0
or, x²+8x-20=0
or, x²+10x-2x-20=0
or, x(x+10)-2(x+10)=0
or, (x+10)(x-2)=0
∴, either, x=-10 or, x=2
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