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Byju's Answer
Standard XII
Mathematics
Equation of Circle with (h,k) as Center
The area of a...
Question
The area of a circle centered at
(
1
,
2
)
and passing through
(
4
,
6
)
is
A
5
π
sq. units
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B
15
π
sq. units
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C
25
π
sq. units
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D
30
π
sq. units
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Solution
The correct option is
A
25
π
sq. units
Coordinates of the centre of the circle
(
x
1
,
y
1
)
=
(
1
,
2
)
and coordinates of the point through which it passes
(
x
2
,
y
2
)
=
(
4
,
6
)
.
We know that the radius of the circle
r
=
√
(
x
2
−
x
1
)
2
+
(
y
2
−
y
1
)
2
=
√
(
4
−
1
)
2
+
(
6
−
2
)
2
=
√
9
+
16
=
5
Therefore, the area of the circle
π
r
2
=
π
(
5
)
2
=
25
π
sq. units
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Similar questions
Q.
The area enclosed by the circle x
2
+ y
2
= 2 is equal to
(a) 4π sq. units
(b)
2
2
π
sq. units
(c) 4π
2
sq. units
(d) 2π sq. units