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Diameter Of A Circle - Practice Questions & MCQ
Edited By admin | Updated on Sep 18, 2023 18:34 AM | #JEE Main
Quick Facts
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7 Questions around this concept.
Solve by difficulty
A circle $\mathrm{C}_1$ passes through the origin O and has a diameter of 4 on the positive x-axis. The line $\mathrm{y}=2 \mathrm{x}$ gives a chord OA of circle $\mathrm{C}_1$. Let $\mathrm{C}_2$ be the circle with OA as a diameter. If the tangent to $\mathrm{C}_2$ at the point A meets the x-axis at P and $\mathrm{y}_{\text {-axis at }} \mathrm{Q}$, then QA : AP is equal to:
The lines and
are diameters of a circle of area 154 sq. units, then the equation of the circle is
Concepts Covered - 1
DIAMETER OF A CIRCLE
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 $x+m y=0$
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