find the equation of. the circle with center (0,0) and passing through (2,-3)
Answers
Answered by
6
Answer:
hey Mate here is your answer
x
2
+
y
2
=
40
See below.
Explanation:
The equation of a circle with center
(
h
,
k
)
and radius
r
is given by
(
x
−
h
)
2
+
(
y
−
k
)
2
=
r
2
. For a circle centered at the origin, this becomes the more familiar equation
x
2
+
y
2
=
r
2
.
Because we know the circle is centered at the origin, i.e.
(
0
,
0
)
, we can use this fact along with the point which the circle passes through
(
−
6
,
−
2
)
to find the radius. This is done using the distance formula.
r
=
√
(
x
2
−
x
1
)
2
+
(
y
2
−
y
1
)
2
Given the points
(
0
,
0
)
and
(
−
6
,
−
2
)
:
r
=
√
(
−
6
−
0
)
2
+
(
−
2
−
0
)
2
=
√
36
+
4
√
40
=
2
√
10
⇒
r
=
2
√
10
.
Therefore, the equation of the circle is given by:
x
2
+
y
2
=
(
2
√
10
)
2
⇒
x
2
+
y
2
=
40
graph{x^2+y^2=40 [-20, 20, -10, 10]}
Step-by-step explanation:
hope it's helpful for you
Similar questions