help@askiitians.com

1800-150-456-789

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)

Provide a better Answer & Earn Cool Goodies

Enter text here...

LIVE ONLINE CLASSES

Prepraring for the competition made easy just by live online class.

Full Live Access

Study Material

Live Doubts Solving

Daily Class Assignments

Ask a Doubt

Get your questions answered by the expert for free

Enter text here...

question mark

What is a binomial expression?

Algebra

1 Answer Available

Last Activity: 10 Month ago(s)

question mark

Can we divide two vectors? If this is possible then how?

Algebra

1 Answer Available

Last Activity: 10 Month ago(s)

question mark

How do you write “the product of 18 and q” as an algebraic expression?

Algebra

1 Answer Available

Last Activity: 10 Month ago(s)

question mark

दहावीच्या आय सी एस इ विद्यार्थ्यांनी पुढे काय करायला पाहिजे

Algebra

0 Answer Available

Last Activity: 1 Year ago(s)

question mark

Find the least number of square tiles by which the floor of a room of dimensions 16.58 m and 8.32 m can be covered completely. why HCF and not LCM as “least” keywor dis given?

Algebra

1 Answer Available

Last Activity: 2 Year ago(s)

View all Questions