Question

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

Answer 1

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"`