question_answer

A circle with centre (a, b) passes through the origin. The equation of the tangent to the circle at the origin is [RPET 2000]

A)            \[ax-by=0\]                              

B)            \[ax+by=0\]

C)            \[bx-ay=0\]                              

D)            \[bx+ay=0\]

Correct Answer: B

Solution :

           Obviously the slope of the tangent will be \[-\left( \frac{1}{b/a} \right)\] i.e., \[-\frac{a}{b}\].                    Hence the equation of the tangent is \[y=-\frac{a}{b}x\ \] i.e., \[by+ax=0\].