Xcosa+ysina=p;a being a paramerter
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Answer:
Step-by-step explanation:
(
a
cos
θ
,
b
sin
θ
)
represents any point on the given ellipse,
x
2
a
2
+
y
2
b
2
=
1
The to this point on the ellipse will be
x
⋅
a
cos
θ
a
2
+
y
⋅
b
sin
θ
b
2
=
1
⇒
x
cos
θ
a
+
y
sin
θ
b
=
1
But the given equation of the tangent is
x
cos
A
+
y
sin
A
=
p
⇒
x
cos
A
p
+
y
sin
A
p
=
1
Comparing these two equations of the tangent we can write
cos
θ
=
a
cos
A
p
And
sin
θ
=
b
sin
A
p
So we have
(
a
cos
A
p
)
2
+
(
b
sin
A
p
)
2
=
cos
2
θ
+
sin
2
θ
=
1
⇒
p
2
=
a
2
cos
2
A
+
b
2
sin
2
A
HOPE THIS HELPS
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