Mathematics - Complex Number Question with Solution | TestHub

$(\mathrm{k}=12)$ locus of z is an ellipse $\frac{(x-11{)}^2}{25}+\frac{(y-4{)}^2}{16}=1$

Equation of tangent is $y-4=m(x-11)+c\Rightarrow c=11m-4$

As $c^2=a^2{m}^2+b^2$ for standard ellipse

$\Rightarrow (11m-4{)}^2=25m^2+16\Rightarrow m=0$ or $m=\frac{11}{12}$

$\therefore \tan \theta =\frac{11}{12}\Rightarrow \theta ={\tan }^{-1}\frac{11}{12}$