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Algebra> Find the real values of the parameter ‘a’...

question mark

Find the real values of the parameter ‘a’ for which atleast one complex number z =x+iy satisfies both the equality
|z-ai|=a+4 and the inequality |z-2| is less than 1 .

saurabh , 10 Years ago

Grade 12th pass

2 Answers

Jitender Singh

Last Activity: 10 Years ago

Ans:
Hello Student,
Please find the answer to your question below
$|z-ai| = a + 4$
$|z-2| \leq 1$

For having atleast one solution for both the equation, the first circle should intersect with 2^ndcircle on the x – axis.
$|x+iy-ai| = a + 4$
$|x+i(y-a)| = a + 4$
$|x+i(y-a)|^{2} = (a + 4)^{2}$
$x^{2}+(y-a)^{2} = (a + 4)^{2}$
Intersection with x-axis, we have
$x^{2}+(0-a)^{2} = (a + 4)^{2}$
$x^{2} = 8a + 16$
$8a + 16 = (3)^{2}$
$8a + 16 = 9$
$a = \frac{-7}{8}$

saurabh

Last Activity: 10 Years ago

first of all $|z-2| \leq 1$ is not right as given in qus this is less than 1 not equal second thing this qus is from resonannce assignment and ans is (-21/10 ,- 5/6)

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