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Question
If the lines 2x − 3y = 5 and 3x − 4y = 7 are the diameters of a circle of area 154 square units, then obtain the equation of the circle.
Solution
We have Area of circle = 154
\[ \Rightarrow r^2 = 49\]
Solving 2x − 3y = 5 and 3x − 4y = 7 we get
x = 1 and y = −1
Now, the equation of the circle is given by
\[ \Rightarrow \left( x - 1 \right)^2 + \left( y + 1 \right)^2 = 49\]
\[ \Rightarrow x^2 + y^2 - 2x + 2y - 47 = 0\]
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