Question:
If the line 2x – y λλ = 0 is a diameter of the circle x2 y2 6x−6y 5=0x2 y2 6x−6y 5=0 then λλ =
Answer:
Given equation of the circle is
x2 + y2 + 6x − 6y + 5 = 0
Center O = (-3, 3)
radius r = √{(-3)2 + (3)2 - 5} = √{9 + 9 - 5} = √13
Since diameter of the circle passes through the center of the circle.
So (-3, 3) satisfies the equation 2x – y + λ = 0
=> -3*2 - 3 + λ = 0
=> -6 - 3 + λ = 0
=> -9 + λ = 0
=> λ = 9
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