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Question
Find the equation of the circle whose centre lies on the positive direction of y - axis at a distance 6 from the origin and whose radius is 4.
Solution
Let (h, k) be the centre of a circle with radius a.
Thus, its equation will be
Thus, the coordinates of the centre are (0, 6).
∴ Equation of the circle = \[\left( x - 0 \right)^2 + \left( y - 6 \right)^2 = a^2\]
Substituting the value of a in equation (1): \[\left( x - 0 \right)^2 + \left( y - 6 \right)^2 = 16\]
\[ \Rightarrow x^2 + y^2 - 12y + 20 = 0\]
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