Question

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

Answer 1

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.

Answer 2

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