CBSE Class 12-science Answered

General equation of circle is

x² + y² + 2gx + 2fy + c = 0  ............................(1)

If the circle as given in eqn.(1)  pases through (1,0) , the we get

2g+c = -1 ...................(2)

If the circle as given in eqn.(1)  pases through (0,1) , the we get

2f+c = -1 ...................(3)

from eqn.(2) and (3) , we get

g = f ..........................(4)

If the circle as given in eqn.(1)  pases through (0,0) , the we get

c = 0 ...................(5)

Using eqn.(5) , we get from equations (2) , (3) and (4) as

g = f = -1/2

Hence equation of circle is

x² + y²  - x - y  = 0  ............................(6)

If the circle as given in eqn.(6)  pases through (2k,3k) , the we get

4k² + 9k² - 2k - 3k = 0

13k² - 5 k = 0

hence we get k = 5/13