Question

find the radius of the circle whose center is 3, 2 passes throgh -5 , 6 ​

Answer 1

Answer:

The general form of the equation of a circle is

(

x

−

h

)

2

+

(

y

−

k

)

2

=

r

2

where

(

h

,

k

)

are the coordinates of the center and

r

is the length of the radius.

We are given that the center is at

(

2

,

6

)

so we need to figure out the length of the radius. Since we know the circle passes through the point

(

3

,

1

)

, we know the radius is just the distance between

(

2

,

6

)

and

(

3

,

1

)

. In the equation, we end up using

r

2

instead of

r

which makes our calculations a bit easier:

Distance

=

r

=

√

(

x

2

−

x

1

)

2

+

(

y

2

−

y

1

)

2

r

2

=

(

x

2

−

x

1

)

2

+

(

y

2

−

y

1

)

2

r

2

=

(

2

−

3

)

2

+

(

6

−

1

)

2

r

2

=

26

Now that we have everything, we just substitute our values into the equation of a circle:

(

x

−

2

)

2

+

(

y

−

6

)

2

=

26

Step-by-step explanation:

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