Show that the product of the lengths of
ht perpendicular segments drawn from
the foci to any tangent line to the ellipse
x2/25 + y2/16 = 1 is equal to 16.
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Answer:
25
x
2
+
16
y
2
=1e=
5
41
ae=
41
Foci S(ae,o)=S(41,o)S(ae,o)=S(
41
,o)
y=mx+
a
2
m
2
b
2
y=mx+
25m
2
−16
P
1
=
∣
∣
∣
∣
∣
∣
m
2
+1
m(
41
)+(−1)(o)+
25m
2
−16
∣
∣
∣
∣
∣
∣
=
∣
∣
∣
∣
∣
∣
m
2
+1
25m
2
−16
∣
∣
∣
∣
∣
∣
P
0
=
∣
∣
∣
∣
∣
∣
m
2
+1
m(−
41
)+(−1)(o)+
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