The centre of the circle which passes through the vertices of the triangle formed by the lines (y=0, y=x ) and (2 x+3 y=10 ), is

Step-by-step solution

Given equation of sides are ( aligned y & =0 (i) y & =x (ii) 2 x+3 y & =10 (iii) aligned ) Solving Eqs. (i) and (iii) to get vertex ' (A ) ' ( A=(5,0) ) Solving (i) and (ii) to get vertex ' (B ) ' (B=(0,0) ) Solving Eqs. (ii) and (iii) to get vertex ' (C ) ' (C=(2,2) ) Let equation of circle be (x^2+y^2+2 g x+2 f y+c=0 ) ...(iv) Since, Eq. (iv) passes through (B(0,0) ) ( C=0 ) Since, Eq. (iv) passes through (A(5,0) ) ( aligned & 25+0+10 g+0+0=0 & g=-5 / 2 aligned ) Eq. (iv) passes through (C(2,2) ) ( gathered 4+4+4