The equation of the circle passing through \((0,0)\) and which makes intercepts \(a\) and \(b\) on the…

The equation of the circle passing through \((0,0)\) and which makes intercepts \(a\) and \(b\) on the coordinate axes is
  1. \(x^2+y^2+a x+b y=0\)
  2. \(x^2+y^2+a x-b y=0\)
  3. \(x^2+y^2-a x+b y=0\)
  4. \(x^2+y^2-a x-b x=0\)

Solution

$\begin{aligned} & \text{Centre }=\left(\frac{a}{2}, \frac{b}{2}\right) \\ & \text{Radius }=\frac{\sqrt{a^{2}+b^{2}}}{2} \end{aligned}$
Equation of circle $\begin{aligned} & \Rightarrow \left(x-\frac{a}{2}\right)^2+\left(y-\frac{b}{2}\right)^2=\frac{a^2+b^2}{4} \\ & \Rightarrow x^2+a^2-a x+y^2+b^2-b y=a^2+b^2 \\ & \Rightarrow x^2+y^2-a x-b y=0 \end{aligned}$

Asked in: AP EAMCET 2020 (17 Sep Shift 1)

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