Complex number z satisfies the equation `||z-5i| + m|z-12i||=n`. Then match the value of m and n in List I with the corresponding locus in List II.

Answer

`a to r; b to p; c to s; d to q;`

Explanation

We have equation`||z-5i|+ m|z-12i|| = n`
a. `m = 1 and n = 13`
`therefore |z - 5i| + |z -12i| = 13`
`or |z-5i| + |z-12i| = |5-12i|`
So, z lies on the line segment joining complex number '5' and '12i'.
b. `m = 1 , n=15`
` therefore |z-5i| + |z- 12i| = 15 gt 13`
So, z lies on the ellispe whose foic are '5' and '12i'.
c. `m =- 1, n=13`
`therefore ||z-5i|-|z- 12i||= 13`
`or ||z-5i|-|z-12i||= |5-12i|`
so, z lies on either of the two rays emanating form '5' and
'12i' and moving in opposite directions.
d. `m = -1 , n = 12 `
`therefore ||z - 5i|-|z - 12i|| = 12 lt 13`
So, lies on the hyperbola whose foci are '5' and '12i' .