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10.1 circle and system of circle — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHS10.1 circle and system of circle1 Mark
MCQ
If a circle passes through the point $(0, 0), (a, 0), (0, b)$ 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
(c) Let the equation of circle be ${x^2} + {y^2} + 2gx + 2fy + c = 0$. Now on passing through the points, we get three equations.

$c = 0$….$(i)$

${a^2} + 2ga + c = 0$….$(ii)$

${b^2} + 2fb + c = 0$….$(iii)$

On solving them, 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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