BITSAT 2019 Paper

(c) Two circles x2+y2 + 2g‌1x + 2f‌1y + c‌1 = 0
and x2+y2 + 2g‌2x + 2f‌2y + c‌2 = 0 cuts
orthogonally if 2g‌1g‌2 + 2f‌1f‌2 = c‌1 + c‌2
Given equations of two circles are
x2+y2 + 2λx + 6y + 1 = 0 ....(i)
x2+y2 + 4x + 2y = 0 ....(ii)
On comparing (i) and (if ) with original equation,
we get
g‌1 = λ, f‌1 = 3, c‌1 = 1 and g‌2 = 2, f‌2 = 1, c‌2 = 0
So, from orthogonality condition, we have
4λ + 6 = 1 ⇒ 4λ = -5
∴ λ = −

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