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Linear Equations in Two Variables

15 find the e...

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15 find the equation of the circle which passes through the vertices of the triangle formed by L1 = x + y +1 =0 ; L2 =3x + y -5 =0 ; L3= 2x + y -5 =0.

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Q. Find the equations of circles which passes through the vertices of the triangle formed by the line
x + y + 1 = 0 , 3x +y - 5 = 0 and 2x + y - 5 = 0 z

Q. The circumcircle of the triangle whose sides are

L_{1} = 3 x + y - 5 = 0, L_{2} = 2 x + y - 3 = 0, L_{3} = 3 x + 2 y - 7 = 0

Find the equation of the circle circumscribing the triangle formed by the lines $L_{1} = 0, L_{2} = 0$ and $L_{3} = 0$

Q. Find the equation of the circle which circumscribes the triangle formed by the lines
(i) x + y + 3 = 0, x − y + 1 = 0 and x = 3
(ii) 2x + y − 3 = 0, x + y − 1 = 0 and 3x + 2y − 5 = 0
(iii) x + y = 2, 3x − 4y = 6 and x − y = 0.

Q. If the lines

L_{1} : λ^{2} x - y - 1 = 0

L_{2} : x - λ^{2} y + 1 = 0

L_{3} : x + y - λ^{2} = 0

pass through the same point the value(s) of

λ

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