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Byju's Answer
Standard XIII
Mathematics
Distance Formula to Find Condition for Co-Linearity
A −a,0 and B ...
Question
A (−a,0) and B (a,0) are two fixed points. The locus of a point P such as
∠
A
P
B
is a right angle, is
A
x
2
+
y
2
=
a
2
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B
x
2
-
y
2
=
a
2
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C
2
x
2
+
y
2
=
a
2
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D
pair of lines
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Solution
The correct option is
A
x
2
+
y
2
=
a
2
Let P (x, y) be the moving point whose locus is required.
L
e
t
A
≡
(
−
a
,
0
)
a
n
d
B
≡
(
a
,
0
)
,
G
i
v
e
n
∠
A
P
B
=
π
2
∴
A
P
2
+
P
B
2
=
A
B
2
⇒
(
x
+
a
)
2
+
y
2
+
(
x
−
a
)
2
+
y
2
=
(
2
a
)
2
⇒
2
x
2
+
2
y
2
+
2
a
2
=
4
a
2
⇒
x
2
+
y
2
=
a
2
Which is the required locus.
Hence, (a) is the correct answer.
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