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Question: If z = (a + 3) + i \(\sqrt{5 - \alpha^{2}}\), then the locus of z is...

If z = (a + 3) + i 5−α2\sqrt{5 - \alpha^{2}}, then the locus of z is

A

An ellipse

B

A circle

C

A parabola

D

A straight line

Answer

A circle

Explanation

Solution

Sol. Let z = x + iy

z = a + 3 + i(5−α2)\sqrt{(5 - \alpha^{2})}

x + iy = a + 3 + i(5−α2)\sqrt{(5 - \alpha^{2})}

x = a + 3

y = (5−α2)\sqrt{(5 - \alpha^{2})}

y = 5−(x−3)2\sqrt{5 - (x - 3)^{2}} Ž y2 = 5 – x2 – 9 + 6x

x2 + y2 – 6x + 4 = 0 (focus is circle)