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Byju's Answer
Standard XII
Mathematics
Normal of a Curve y = f(x)
Equation of c...
Question
Equation of common tangent to the parabola
x
2
−
y
+
2
=
0
and ellipse
4
x
2
+
9
y
2
=
36
is
A
y
=
x
+
2
√
13
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B
y
=
x
−
2
√
13
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C
y
=
2
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D
y
=
−
3
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Solution
The correct option is
D
y
=
2
x
2
=
y
−
2
...(1)
4
x
2
+
9
y
2
=
36
...(2)
Solving (1) and (2):
4
(
y
−
2
)
+
9
y
2
=
36
⇒
y
=
2
and
y
=
−
22
9
At
y
=
2
,
⇒
x
=
0
For
y
=
−
22
9
,
x
2
=
negative.
Therefore, both curves touch each other at
(
0
,
2
)
.
The tangent will thus be parallel to the
X
-axis and passing through
(
0
,
2
)
Thus equation of common tangent is
y
=
2.
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0
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Equation of common tangent to ellipse
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+
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=
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,
and hyperbola
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−
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is
Q.
Statement-
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:
An equation of a common tangent to the parabola
y
2
=
16
√
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and the ellipse
2
x
2
+
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=
4
is
y
=
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√
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Statement-
2
:
If the line
y
=
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x
+
4
√
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m
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(
m
≠
0
)
is a common tangent to the parabola
y
2
=
16
√
3
x
and the ellipse
2
x
2
+
y
2
=
4
, then
m
satisfies
m
4
+
2
m
2
=
24
.
Q.
For circles
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+
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−
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and
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equation of all the common tangents are:
Q.
Statement-
1
: An equation of a common tangent to the parabola
y
2
=
16
√
3
x
and the ellipse
2
x
2
+
y
2
=
4
is
y
=
2
x
+
2
√
3
Statement-
2
: If the line
y
=
m
x
+
4
√
3
m
,
(
m
≠
0
)
is a common tangent to the parabola
y
²
=
16
√
3
x
and the ellipse
2
x
2
+
y
2
=
4
then
m
satisfies:
m
4
+
2
m
2
=
24.
Q.
Statement 1: An equation of a common tangent to the parabola
y
2
=
16
√
3
x
and the ellipse
2
x
2
+
y
2
=
4
is
y
=
2
x
+
2
√
3
.
Statement 2: If the line
y
=
m
x
+
4
√
3
m
,
(
m
≠
0
)
is a common tangent to the parabola
y
2
=
16
√
3
x
and the ellipse
2
x
2
+
y
2
=
4
, then
m
satisfies
m
4
+
2
m
2
=
24
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