Show that the product of the lengths of the
perpendicular segments drawn from the
foci to any tangent line to the ellipse
x + y2 = 1 is equal to 16.
16
25
Answers
Answered by
1
Answer:
+
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)+
25m
2
−
16
∣
∣
∣
∣
∣
∣
=
∣
∣
∣
∣
∣
∣
m
2
+1
25m
2
−16
−
41
m
∣
∣
∣
∣
∣
∣
P
1
P
2
=
∣
∣
∣
∣
∣
∣
m
2
+1
25m
2
−16
+
41
m
∣
∣
∣
∣
∣
∣
×
∣
∣
∣
∣
∣
∣
m
2
+1
25m
2
−16−
41
m
∣
∣
∣
∣
∣
∣
=
∣
∣
∣
∣
∣
m
2
+1
25m
2
−16−41m
2
∣
∣
∣
∣
∣
=
∣
∣
∣
∣
∣
m
2
+1
−16m
2
−16
∣
∣
∣
∣
∣
=16
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