Question

Statement I.: The equation $z\overline{z}+\overline{a}z+a\overline{z}+\lambda =0$, where a is a complex number, represents a circle in Argand plane if $\lambda$ is real.

Statement-ll: The radius of the circle $z\overline{z}+\overline{a}z+a\overline{z}+\lambda =0is\sqrt{\lambda -a\overline{a}}$

• A. Both A and R are true and R is the correct explanation of A
• B. Both A and R are true but R is not the correct explanation of A
• C. A is true, R is false
• D. A is false, R is true

Answer 1

Answer: (C)

A is true, R is false

b'$z=x+iy,a=\alpha +i\beta$
$x^2+y^2+(\alpha -i\beta )(x+i\beta )(\lambda -iy)\alpha \succ =0$
$x^2+y^2+2\alpha x+2\beta y+\lambda =0$
$(x+\alpha {)}^2+(y+\beta {)}^2={\alpha }^2+{\beta }^2=lambda$
Represents earde.
$=(\lambda -(\alpha +i\beta \left)\right(\alpha -i\beta ){)}^2$
Radius$=\sqrt{\lambda -a\overline{a}}$'