8. Find the radius of the Circle 45 x2 + 45 y2 - 60 x + 36 y + 19 = 0
9. 1 + 2 + 3 +.............+n=
Answers
Answer:
Step-by-step explanation:
Center:
(
3
,
2
)
XXXXX
Radius:
5
XXX
(see below for method)
Explanation:
An equation in the form:
XXX
(
x
−
a
)
2
+
(
y
−
b
)
2
=
r
2
is the standard form for the equation of a circle with center
(
a
,
b
)
and radius
r
.
Lets try to convert the given equation:
XXX
x
2
+
y
2
−
6
x
−
4
y
−
12
=
0
into the standard form for the equation of a circle.
Group the
x
and
y
terms separately and "move" the constant to the right side of the equation:
XXX
x
2
−
6
x
+
3
2
+
y
2
−
4
y
+
2
2
=
12
Complete the square for each of
x
and
y
XXX
x
2
−
6
x
+
3
2
+
y
2
−
4
y
+
2
2
=
12
+
3
2
+
2
2
Write the left side as the sum of two squared binomials
and simplify the result on the right side
XXX
(
x
−
3
)
2
+
(
y
−
2
)
2
=
25
Express the right side as a square.
XXX
(
x
−
3
)
2
+
(
y
−
2
)
2
=
5
2
...the equation for a circle with center
( Center:
(
3
,
2
)
XXXXX
Radius:
5
XXX
(see below for method)
Explanation:
An equation in the form:
XXX
(
x
−
a
)
2
+
(
y
−
b
)
2
=
r
2
is the standard form for the equation of a circle with center
(
a
,
b
)
and radius
r
.
Lets try to convert the given equation:
XXX
x
2
+
y
2
−
6
x
−
4
y
−
12
=
0
into the standard form for the equation of a circle.
Group the
x
and
y
terms separately and "move" the constant to the right side of the equation:
XXX
x
2
−
6
x
+
3
2
+
y
2
−
4
y
+
2
2
=
12
Complete the square for each of
x
and
y
XXX
x
2
−
6
x
+
3
2
+
y
2
−
4
y
+
2
2
=
12
+
3
2
+
2
2
Write the left side as the sum of two squared binomials
and simplify the result on the right side
XXX
(
x
−
3
)
2
+
(
y
−
2
)
2
=
25
Express the right side as a square.
XXX
(
x
−
3
)
2
+
(
y
−
2
)
2
=
5
2
...the equation for a circle with center
(
3
,
2
)
and radius
5
3
,
2
)
and radius
5