Tangents pa and pb are drawn to the ellipse x^2/16 + y^2/9=1 from the point (0,5). Find the area of triangle pab
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Answer:
Given, Equation of the ellipse,
16
x
2
+
9
y
2
=1
∴ Chord of contact,
16
xx
1
+
9
yy
1
=1
⇒
16
x×0
+
9
y×5
=1
⇒y=
5
9
Putting y=
5
9
in the above equation of the ellipse,
16
x
2
+
9
(
5
9
)
2
=1
⇒
16
x
2
=
25
16
⇒x
2
=
25
16×16
⇒x=±
5
16
So, A=(
5
16
,
5
9
),B=(−
5
16
,
5
9
),P=(0,5)
Since, △PAB is isosceles with base AB
∴Height=(5−
5
9
)units
=
5
16
units
∴ Area of △PAB=
2
1
×Base×Height
=
2
1
×(
5
16
+
5
16
)×
5
16
=
25
256
squareunits.
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