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Byju's Answer
Standard XII
Mathematics
Standard Equation of Ellipse
If a tangent ...
Question
If a tangent of slope 2 of the ellipse
x
2
a
2
+
y
2
b
2
=
1
is normal to the circle
x
2
+
y
2
+
4
x
+
1
=
0
then the maximum value of ab is
A
2
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B
4
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C
6
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D
Can’t be found
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Solution
The correct option is
B
4
A tangent of slope 2 is
y
=
2
x
±
√
4
a
2
+
b
2
,this is normal to
x
2
+
y
2
+
4
x
+
1
=
0
then
0
=
−
4
±
√
4
a
2
+
b
2
⇒
4
a
2
+
b
2
=
16
u
s
i
n
g
A
.
M
.
≥
G
.
M
.
,
W
e
g
e
t
a
b
≤
4
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0
Similar questions
Q.
If a tangent of slope 2 of the ellipse
x
2
a
2
+
y
2
b
2
=
1
is normal to the circle
x
2
+
y
2
+
4
x
+
1
=
0
then the
maximum value of
ab
is
Q.
If a tangent to the ellipse
x
2
a
2
+
y
2
b
2
=
1
having slope
2
is normal to the circle
x
2
+
y
2
+
4
x
+
1
=
0
,
then the maximum value of
a
b
is
Q.
Slope of the common tangent to the ellipses
x
2
a
2
+
b
2
+
y
2
b
2
=
1
,
x
2
a
2
+
y
2
a
2
+
b
2
=
1
is:
Q.
A
line touches the ellipse
x
2
a
2
+
y
2
b
2
=
1
and the circle
x
2
+
y
2
=
r
2
Then the slope
m
of the common tangent is given by
m
2
=
Q.
Assertion :The angle of intersection between the ellipse
x
2
a
2
+
y
2
b
2
=
1
and the circle
x
2
+
y
2
=
a
b
is
tan
−
1
(
b
−
a
)
√
a
b
Reason: The point of intersection of the ellipse
x
2
a
2
+
y
2
b
2
=
1
and the circles
x
2
+
y
2
=
a
b
is
⎛
⎝
√
a
2
b
a
+
b
,
√
a
b
2
a
+
b
⎞
⎠
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