A circle with centre $(a, b)$ passes through the origin. The equation of the tangent to the circle at the origin is

a x - b y = 0

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a x + b y = 0

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b x - a y = 0

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b x + a y = 0

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Solution

The correct option is B $a x + b y = 0$
Slope of the line joining the centre and the origin is $\frac{b}{a}$
The slope of the tangent will be $- ⎛ ⎜ ⎜ ⎜ ⎝ \frac{1}{\frac{b}{a}} ⎞ ⎟ ⎟ ⎟ ⎠$ , i.e., $- \frac{a}{b}$ .
Hence, the equation of the tangent is $y = - \frac{a}{b} x + 0$ i.e. $b y + a x = 0$ .

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