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Question
If the equations of two diameters of a circle are 2x + y = 6 and 3x + 2y = 4 and the radius is 10, find the equation of the circle.
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Solution
Let (h, k) be the centre of a circle with radius a.
Thus, its equation will be
The intersection point of 2x + y = 6 and 3x + 2y = 4 is (8, −10).
The diameters of a circle intersect at the centre.
Thus, the coordinates of the centre are (8, −10).
∴ h = 8, k = −10
Thus, the equation of the required circle is
Also, a = 10
Substituting the value of a in equation (1):
\[\Rightarrow x^2 + y^2 - 16x + 64 + 100 + 20y = 100\]
\[ \Rightarrow x^2 + y^2 - 16x + 20y + 64 = 0\]
Hence, the required equation of the circle is
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