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Byju's Answer
Standard X
Mathematics
Distance between Two Points on the Same Coordinate Axes
Show that, if...
Question
Show that, if
x
2
+
y
2
=
1
, then the point
(
√
x
2
+
y
2
,
√
1
−
x
2
−
y
2
)
is at a distance
1
unit from the origin.
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Solution
Given
x
2
+
y
2
=
1
.
Now the distance of the point
(
√
x
2
+
y
2
,
√
1
−
x
2
−
y
2
)
from the origin is:
√
(
√
x
2
+
y
2
−
0
)
2
+
(
√
1
−
x
2
−
y
2
−
0
)
2
=
√
x
2
+
y
2
+
1
−
x
2
−
y
2
=
1
.
Hence, Proved.
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Similar questions
Q.
The equation of the circle in the first quadrant touching each coordinate axes at a distance of one unit from the origin is
(a) x
2
+ y
2
– 2x – 2y + 1 = 0
(b) x
2
+ y
2
– 2x – 2y – 1 = 0
(c) x
2
+ y
2
– 2x – 2y = 0
(d) x
2
+ y
2
– 2x + 2y – 1 = 0