Coordinate Geometry
> Question
VSA
2 marks
Year: 2025
Medium
CBSE Class 10
coordinate-geometry
distance-formula
circle
Question
The coordinates of the centre of a circle are
(
2
a
,
a
−
7
)
. Find the value(s) of
a
if the circle passes through the point
(
11
,
−
9
)
and has diameter
10
2
units.
Solution
1
Radius
=
5
2
units. Using distance formula:
(
2
a
−
11
)
2
+
(
a
−
7
+
9
)
2
=
(
5
2
)
2
=
50
+0.5 marks
2
(
2
a
−
11
)
2
+
(
a
+
2
)
2
=
50
⇒
4
a
2
−
44
a
+
121
+
a
2
+
4
a
+
4
=
50
⇒
5
a
2
−
40
a
+
75
=
0
⇒
a
2
−
8
a
+
15
=
0
+1 mark
3
(
a
−
5
)
(
a
−
3
)
=
0
⇒
a
=
5
or
a
=
3
+0.5 marks
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