Question

Locus of midpoints of chords of hyperbola 14. 9x² 25y² = 225, such that tangents at extrimities of these chords intersect at right

angle, is​

Answer 1

Step-by-step explanation:

Let (x

1

,y

1

) be the point of intersection of perpendicular tangents so that (x

1

,y

1

) lies on director circle ∴x

1

2

+y

1

2

=a

2

+b

2

...(1)

Then the chord will be chord of contact of (x

1

,y

1

)

∴

a

2

xx

1

+

b

2

yy

1

=1...(2)

If its mid-point is (h,k), then its equation is

a

2

hx

+

b

2

ky

=

a

2

h

2

+

b

2

k

2

...(3)

Compare (2) and (3) and find x

1

,y

1

and put in (1)

∴ Locus of (h,k) is (

a

2

x

2

+

b

2

y

2

)

2

(a

2

+b

2

)=x

2

+y

2