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The Circle — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSThe Circle3 Marks
Question
Find the equation of the circle having $(1, -2)$ as its centre and passing through the intersection of the lines $3x + y = 14$ and $2x + 5y = 18$.
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Answer

Intersection of 3x + y = 14 and 2x +5y= 18 is Obtained by solving two equations. x = 4 and y = 2 Point (4,2) is on circle, hence~ distance from centre (1,-2) = Radius $=\sqrt{(1-4)^2+(-2-1)^2}$
$=\sqrt{9+16}$
 $=5$ Equation of the circle with centre (4,2) and radius 5 is, $(x - 1)^2+ (y + 2)^2 = 25 x^2 - 2x + 1 + y^2 + 4y + 4 = 25 x^2 + y^2 - 2x + 4y - 20 = 0$

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