a chord of the ellipse x^2/16+y^2/9=1 passing through the positive focus subtends an angle of 90 at centre .the coordinates of point at where it goes on to intersect the y axis 1
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0
Answer:
Let (h,k) be the mid-point of a chord passing through the positive end of the minor axis of the ellipse
a
2
x
2
+
b
2
y
2
=1. Then, the equation of the chord is
a
2
hx
+
b
2
ky
−1=
a
2
h
2
+
b
2
k
2
−1(∵T=S
1
)
⇒
a
2
hx
+
b
2
ky
=
a
2
h
2
+
b
2
k
2
It passes through (0,b)
∴0+
b
2
kb
=
a
2
h
2
+
b
2
k
2
⇒
b
k
=
a
2
h
2
+
b
2
k
2
Hence, locus of a point is
b
y
=
a
2
x
2
+
b
2
y
2
which represents an equation of ellipse.
Answered by
4
Answer:
The locus of the middle point of chords of an ellipse
passing through
in another ellipse E. The coordinates of the foci of the ellipse E, is
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