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Byju's Answer
Standard XII
Mathematics
Length of Intercept Made by a Circle on a Straight Line
If a chord of...
Question
If a chord of a circle
x
2
+
y
2
=
32
makes equal intercepts of length
l
on the co-ordinate axes, then
A
ℓ
<
8
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B
ℓ
<
16
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C
ℓ
>
8
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D
ℓ
>
16
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Solution
The correct option is
A
ℓ
<
8
Since the chord makes equal intercepts of length
l
on coordinate axes, so the equation can be written as :-
x
±
y
=
±
l
The length of
⊥
from centre
(
0
,
0
)
to the chord must be less than radius
∣
∣
∣
±
l
√
2
∣
∣
∣
>
√
32
∴
l
2
<
64
l
<
8
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0
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