Equation of a locus 3 units from a circle's circumference

[aisha]

CHECK PLZ HELP a little

Determine the equation of the following locus.

1)-Locus of points that are 10 units from the origin.
x^2+y^2=100?

2-The points 3 units from the circumference of the circle with centre (0, 0) and radius 5 units
What does the 3 units from the circumference mean? is the equation x^2+y^2=25?

Are these two correct I am not sure about the second one?

 

[aisha]

HELP! are my answers correct?

 

[Data]

What does the 3 units from the circumference mean?

it means 3 units from the circle. The question asks for the set of points a distance of three units from the circle defined by $x^2 +y^2 = 25$.

 

[aisha]

$$x^2+y^2=8^2?$$ since the radius is 5+3?

 

[Data]

That's half of it.

Here's a hint: think INside the box (or in this case, the circle!)

 

[aisha]

and another locus is x^2+y^2=2^2

I should simplify both of these to 4 and 64 right?

 

[Data]

Yep, that's fine~