Question

3. Find the equation of the circle passing through (0,0) and making intercepts a and
b on the coordinate axes.​

Answer 1

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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 = 0

0 + 0 + 0 + 0 + C = 0

C = 0 -------(1)

when point (a,0)

(a)² + (0)² + 2g(a) + 2f(0) + C = 0

a² + 2ag + C = 0

from equation (1)

a² + 2ag = 0

a(a + 2g) = 0

g = -a/2

when point ( 0, b)

(0)² + (b)² + 2g(0) + 2f(b) + C = 0

b² + 2fb + C = 0

f = -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