Question

20. The equation of the locus of a point which moves so that its distance from the point
(ak, 0) is k times its distance from the point(a/k,0) is:​

Answer 1

Correct option is

D

x

2

+y

2

=a

2

Let the point on locus be (x,y)

∴ (x−ak)

2

+y

2

=k

2

[(x−a/k)

2

+y

2

]

⇒x

2

+a

2

k

2

−2axk+y

2

=k

2

[x

2

+

k

2

a

2

−2

k

ax

+y

2

]

⇒x

2

+y

2

=k

2

[x

2

+y

2

]−a

2

k

2

+a

2

⇒[x

2

+y

2

][k

2

−1]=a

2

[k

2

−1]

⇒x

2

+y

2

=a

2

[D]