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Question: The circle whose centre is the point (3, –1) and cuts off a chord of length 6 on the line 2x + 5y + ...

The circle whose centre is the point (3, –1) and cuts off a chord of length 6 on the line 2x + 5y + 18 = 0 is

A

(x + 3)2 + (y + 1)2 = 38

B

(x –3)2 + (y + 1)2 = 38

C

(x –3)2 + (y –1)2 = 38

D

None of these

Answer

(x –3)2 + (y + 1)2 = 38

Explanation

Solution

AB : 2x –5y + 18 = 0

P = CL =6+5+1829\frac{6 + 5 + 18}{\sqrt{29}}= 29\sqrt{29}

Also AL = 1/2 AB = 3

\ a2 = AL2 + CL2 = 38

So equation of circle (x –3)2 + (y +1)2 = 38