Question 774946
a point is at a distance 4 sqrt of 2 units from (-3/2,-5/2) and at a distance 2 sqrt of 5 units from (9/2,-5/2), find the point
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Draw a circle around each given point with the radius = the given distance.
The points (2 of them) will be the intersections of the circles.
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a distance 4 sqrt of 2 units from (-3/2,-5/2) --> {{{(x + 3/2)^2 + (y + 5/2)^2 = 32}}}
a distance 2 sqrt of 5 units from (9/2,-5/2) --> {{{(x - 9/2)^2 + (y + 5/2)^2 = 20}}}
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Lucky the y terms are equal
{{{(x + 3/2)^2 + (y + 5/2)^2 = 32}}}
{{{(x - 9/2)^2 + (y + 5/2)^2 = 20}}}
------------------------------ Subtract
{{{(x + 3/2)^2 - (x - 9/2)^2 = 12}}}
{{{(2x + 3)^2 - (2x - 9)^2 = 48}}}
{{{(4x^2 + 12x + 9) - (4x^2 - 36x + 81) = 48}}}
{{{48x - 72 = 48}}}
x = 5/2
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Sub for x into either eqn, find 2 values for y