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Byju's Answer
Standard XII
Mathematics
Convexity
The minimum d...
Question
The minimum distance of a point on the curve
y
=
x
2
−
4
from the origin is:
A
√
15
2
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B
√
19
2
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C
√
19
2
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D
√
15
2
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Solution
The correct option is
A
√
15
2
Let take
(
x
1
,
y
1
)
be the point on the curve
y
=
x
2
−
4
(1)
Another point is
(
0
,
0
)
Distance
=
√
(
x
1
−
0
)
2
+
(
y
1
−
0
)
2
(2)
(Distance)
2
=
(
x
1
)
2
+
(
y
1
)
2
Using
(
1
)
(Distance)
2
=
y
+
4
+
y
2
Differentiate it to give
2
y
+
1
=
0
y
=
−
1
2
From
(
1
)
−
1
2
+
4
=
x
2
x
=
±
√
7
√
2
Since
x
and
y
co -ordinates are given.
MInimum Distance
=
√
=
√
1
5
2
Suggest Corrections
0
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