The equation of the circle having centre (1, –2) and passing through the point of intersection of the lines 3x + y = 14 and 3x + 5y = 18 is
(a) x² + y² – 2x + 4y – 20 = 0
(b) x² + y² – 2x – 4y – 20 = 0
(c) x² + y² + 2x – 4y – 20 = 0
(d) x² + y² + 2x + 4y – 20 = 0

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Solution

correction
Since center of the circle is (1, −2) equation of circle is
(x − 1)² + (y + 2)²= r²
Since above circle passes through points of intersection of 3x + y = 14 and correction
3x + 5y = 18
4y = −4
i.e. y = 1
$i . e . x = \frac{13}{3}$

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