Question

The equation |z - 5i| $÷$ |z + 5i| = 12, where z = x + iy, represents a/an

• A. circle
• B. ellipse
• C. parabola
• D. no near curve

Answer 1

The correct option is A circle

Given, $\frac{|z-5i|}{|z+5i|}=12$

$\Rightarrow \frac{x^2+(y-5{)}^2}{x^2+(y+5{)}^2}=12$

$\Rightarrow x^2+y^2+25-10y=12[x^2+y^2+25+10y]$

$\Rightarrow 11x^2+11y^2+130y+275=0.$

Which represents the equation of a circle.