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If ( - 1, 3) and (∝, β) are the extremities of the diameter of the circle x2 + y2 – 6x + 5y – 7 = 0, find the coordinates (∝, β).

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Given x2 + y2 – 6x + 5y – 7 = 0

Centre(3,-\(\frac{5}{2}\))

As ( - 1, 3) & (∝, β) are the 2 extremities of the diameter, using mid - point formula we can write

\(\frac{∝-1}{2}\) = 3

⇒ ∝ = 7

and  \(\frac{\beta+3}{2}\) = \(-\frac{5}{2}\) 

⇒ β = -8

(∝, β) = (7, - 8)

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