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  • Find the equation of a circle whose centre is (3, –1) and which cuts off a chord of length 6 units on the line 2x – 5y + 18 = 0.

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

Answers (1)

Given centre of the circle O(3, -1)

 Chord of the circle is AB

  Given that equation of AB is 2x-5y+18=0 

 Perpendicular distance from O to AB is OP=  \left | \frac{2(3)-5(-1)+18}{\sqrt{4+25}} \right |=\frac{29}{\sqrt{29}}=\sqrt{29}

OB2=OP2+PB2

OB2=29+9=38

OB=\sqrt{38}

Equation of the circle is (x-3)2+(y+1)2=38

x2+y2-6x+2y=28

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