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Byju's Answer
Standard XII
Mathematics
Distance Formula
Show that the...
Question
Show that the two parabolas
x
2
+
4
a
(
y
−
2
b
−
a
)
=
0
and
y
2
=
4
b
(
x
−
2
a
+
b
)
intersect at right angles at a common end of the latus rectum
of each.
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Solution
d
y
d
x
=
y
′
x
2
+
4
a
(
y
−
2
b
−
a
)
=
0
...............(1)
diffrentiate the eqn.
2
x
+
4
a
y
′
=
0
y
′
=
m
=
−
x
2
a
y
2
=
4
b
(
x
−
2
a
+
b
)
..........(2)
diffrentiate the eqn.
2
y
y
′
=
4
b
y
′
=
n
=
2
b
y
solving eqn (1) & (2)
(
2
a
,
2
b
)
let
θ
be the angle at intersection point
m
×
n
=
−
x
.2
b
y
.2
a
=
−
2
a
.2
b
2
b
.2
a
=
−
1
⇒
θ
=
90
∘
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0
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Q.
Angle between the parabolas
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