The center of a circle is at (2, −5) and its radius is 12.
what is the equation of the circle?
a) (x−2)2+(y+5)2=24
b) (x+2)2+(y−5)2=24
c) (x+2)2+(y−5)2=144
d) (x−2)2+(y+5)2=144

last option

step-by-step explanation:

given that δdef is right and isoceles,

assuming that side df is the hypotenuse means that de an ef are the other 2 sides that intersect at 90° and are of equal length.

because they are of equal length, we can say that they are congruent

because they intersect at 90°, their slopes must be opposite reciprocals.

only the last option satisfies these conditions.