13. Find the equation of the circle passing through (0,0)and making in

1.	13. Find the equation of the circle passing through (0,0)and making intercepts a and b on the co-ordinate axes.d br the intercents made by the circle on the co
Answer» The circle intercept the co-ordinate axes at a and b. it means x - intercept at ( a, 0) and y-intercept at (0, b) . now, we observed that circle passes through points (0, 0) , (a, 0) and (0, b) . we also know, General equation of circle is x² + y² + 2gx + 2fy + C = 0 when point (0,0) (0)² + (0)² + 2g(0) + 2f(0) + C = 00 + 0 + 0 + 0 + C = 0 C = 0 -------(1) when point (a,0) (a)² + (0)² + 2g(a) + 2f(0) + C = 0a² + 2ag + C = 0from equation (1) a² + 2ag = 0 a(a + 2g) = 0g = -a/2 when point ( 0, b)(0)² + (b)² + 2g(0) + 2f(b) + C = 0b² + 2fb + C = 0f = -b/2 now, equation of circle is x² + y² + 2x(-a/2) + 2y(-b/2) + 0 = 0 { after putting values of g, f and C }x² + y² -ax -by = 0

13. Find the equation of the circle passing through (0,0)and making intercepts a and b on the co-ordinate axes.d br the intercents made by the circle on the co

Answer»

The circle intercept the co-ordinate axes at a and b. it means x - intercept at ( a, 0) and y-intercept at (0, b) .

now, we observed that circle passes through points (0, 0) , (a, 0) and (0, b) .

we also know, General equation of circle is x² + y² + 2gx + 2fy + C = 0

when point (0,0) (0)² + (0)² + 2g(0) + 2f(0) + C = 00 + 0 + 0 + 0 + C = 0 C = 0 -------(1)

when point (a,0) (a)² + (0)² + 2g(a) + 2f(0) + C = 0a² + 2ag + C = 0from equation (1) a² + 2ag = 0 a(a + 2g) = 0g = -a/2

when point ( 0, b)(0)² + (b)² + 2g(0) + 2f(b) + C = 0b² + 2fb + C = 0f = -b/2

now, equation of circle is x² + y² + 2x(-a/2) + 2y(-b/2) + 0 = 0 { after putting values of g, f and C }x² + y² -ax -by = 0