Question

pls help me with this question pls a circle has a radius 3 units and its centre lies on the line y=x-1 if it passes through the point (7,3) find its general equation​

Answer 1

Answer:

Let the centre of the circle be (α , β).

It lies on the line y = x − 1

=> β = α − 1.

Hence the centre is (α , α − 1)

=> The equation of the circle is

(x − α)2 + (y − α + 1)2 = 9

It passes through (7, 3)

=> (7 − α)2 + (4 − α)2 = 9

=> 2α2 − 22α + 56 = 0

=> α2 − 11α + 28 = 0

=> (α − 4) (α − 7) = 0

=> α = 4, 7.

Hence the required equations are x2 + y2 − 8x − 6y + 16 = 0 and x2 + y2 − 14x − 12y + 76 = 0.

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