The equation of the circle passing through the points 0-0-0- b and a - b is - x2-y2-a x-b y-0- x2-y2-a x-b y-0- x2-y2-a x-b y-0D- x2-y2-a x-b y-0

The correct option is C Equation of circle passing through (0, 0) is x^2 + y^2 + 2gx + 2fy = 0 ………… (i) Also, circle (i) is passing through (0, b) and (a, b) ...

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Standard XII

Mathematics

Obtaining Centre and Radius of a Circle from General Equation of a Circle

The equation ...

Question

The equation of the circle passing through the points (0, 0), (0, b) and (a, b) is

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Solution

The correct option is C
Equation of circle passing through (0, 0) is
$x^{2} + y^{2} + 2 g x + 2 f y = 0 \dots \dots \dots \dots (i)$
Also, circle (i) is passing through (0, b) and (a, b)
$∴ f = - \frac{b}{2} a n d x^{2} + y^{2} + 2 a g + 2 (- \frac{b}{2}) b = 0$
$\Rightarrow g = - \frac{a}{2}$
Hence the equations of circle is, $x^{2} + y^{2} - a x - b y = 0.$

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