How do you write the equation of the locus of all points in the coordinate plane 10 units from (–6, 9)?

1 Answer
Jim G.
Oct 6, 2016

circle with equation #(x+6)^2+(y-9)^2=100#

Explanation:

The points will lie on the circumference of a circle with centre (-6 ,9) and radius of 10.
The standard form of the equation of a circle is.

#color(red)(bar(ul(|color(white)(a/a)color(black)((x-a)^2+(y-b)^2=r^2)color(white)(a/a)|)))#
where (a ,b) are the coordinates of the centre and r, the radius.

here a = -6 , b = 9 and r = 10

#(x-(-6))^2+(y-9)^2=10^2#

#rArr(x+6)^2+(y-9)^2=100" is the equation of the locus"#

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