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Circle — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsCircle2 Marks
MCQ
If a circle passes through the points (0, 0), (a, 0), (0, b), then its centre is
  • A
    (a, b)
  • B
    (b, a)
  • ✓
    $\left(\frac{a}{2}, \frac{b}{2}\right)$
  • D
    $\left(\frac{b}{2},-\frac{a}{2}\right)$
✓

Answer

Correct option: C.
$\left(\frac{a}{2}, \frac{b}{2}\right)$
(C)
Let the equation of circle be
$x^2+y^2+2 g x+2 f y+c=0$
Now on passing through the given points, we get three equations
$c=0$ ...(i)
$a^2+2 g a+c=0$....(ii)
$b^2+2 f b+c=0$ ....(iii)
Solving equations (i), (ii) and (iii), we get
$g=-\frac{a}{2}, f=-\frac{b}{2}$
Hence, the centre is $\left(\frac{ a }{2}, \frac{b}{2}\right)$.

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