1. identify the centers and radii of the following circles.
a. (x+25)^2+y^2=1
b. x^2+2x+y^2−8y=8
c. x^2−20x+y^2−10y+25=0
d. x^2+y^2=19
e. x^2+x+y^2+y=−1/4

a)

b)

c)

d)

e)

Step-by-step explanation:

the general equation of a circle is can be represented in two forms

here,

the centre is:

radius is:

here,

the centre is:

radius is:

Given these two forms we can solve the questions:

a)

this resembles the first equation of the circle hence we can compare them.

for center: we can see that +25 is the place of '-a', there is nothing in the place of b.

solve for  a

similarly,

the center is

for radius:

, we'll not take '-1' since that negative numbers don't apply to lengths.

b)

we can clearly see that this resembles the second general equation. Hence by comparison we can find +2x is in the place of +2gx, and solve for g.

similarly

the centre of the circle is denoted by

for radius:

side note: the value of 'c' can be found if we simply move 8 from the right hand side of the equation to the left.

c)

we'll do these in the same manner as (b)

the centre of the circle is denoted by

for radius:

d)

this is easy in the sense that both general equations apply here. We can either say since there is no 2gx and 2fy term, both g and f are zeros hence the centre is (0,0)

or we can also say there's no 'a' and 'b', hence the centre is (0,0).

the centre is:

the radius can also be found through any of the two equations, but to keep it short we'll just use:

e)

this is one is again similar to the second equation.

for centre:

the centre of the circle is denoted by

for radius:

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step-by-step explanation: