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The locus of centre of circle which touches the circle $| z - 4 i | = 4 a n d | z - 3 | = 1$ externally is a conic C. Which of the following is/are correct for conic C ?

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distance between foci is $\frac{5}{3}$

Length of latusrectum is $\frac{16}{3}$

Length of latusrectum is 16

distance between foci is 5

answer is A, D.

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Detailed Solution

Locus of centre is hyperbola Whose foci are (0,4), (3,0)

2ae=5,2a=3 Therefore e=5/3.

$b^{2} = a^{2} e^{2} - a^{2} = \frac{25}{4} - \frac{9}{4} = 4 . L a t u s r e c t u m = \frac{2 b^{2}}{a} = \frac{8}{3 / 2} = \frac{16}{3}$

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