Gujarat BoardEnglish MediumSTD 11 ScienceMATHSThe Circle3 Marks
Question
Find the equation of the circle which passes through $(3, -2), (-2, 0)$ and has its centre on the line $2x - y = 3$
✓
Answer
A circle pass Ing through $P(3,-2)$ and $Q(-2,0)$ and having its centre on $2 x-y=3$. Let the equation of the circle be $x^2$ $+y^2+2 g x+2 f y+c=0$. Since the circle passes through $(3,-2)$ andAlso $(-2,0)$ therefore $9+4+6 g-4 f+c=0 . . . . . .$.
(1) $4+0-4 \mathrm{~g}+0+\mathrm{c}=0$.
(2) Also the centre of the circle lies on $2 x-y=3-2 g+f=3$
(3) Solving equallons
(1), (2) and (3), we get $g=\frac{3}{2}, f=6$ and $c=2$ Therefore the equation of the circle is $x^2+y^2+3 x+12 y+2=0$
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