Diameter Of A Circle - Practice Questions & MCQ

 DIAMETER OF A CIRCLE

The locus of the mid-points of a system of parallel chords of a circle is known as the diameter of the circle.
The diameter of a circle always passes through the centre of a circle and perpendicular to the parallel chords Let the equation of the circle be $x^2+y^2=a^2$ and equation of parallel chord $A B$ is, $\quad \mathrm{y}=\mathrm{mx}+\mathrm{c}$.

Equation of any diameter to the given circle is perpendicular to the given parallel chord is $m y+x+$ $\lambda=0$ which passes through the centre $(0,0)$ of a circle.

$
\begin{aligned}
& m \cdot 0+0+\lambda=0 \\
& \lambda=0
\end{aligned}
$
Hence, the required equation of the diameter is $x+m y=0$