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  • Find the equation of a circle passing through the point (7, 3) having radius 3 units and whose centre lies on the line y = x – 1.

Find the equation of a circle passing through the point (7, 3) having radius 3 units and whose centre lies on the line y = x – 1.

Answers (1)

Given that circle passes through the point A(7,3) and its radius is 3   

 Therefore centre of the circle is C(h,h-1)

  Now, radius of the circle is AC=3 

(h-7)2+(h-1-3)2=32

2h2-22h+56=0

h2-11h+28=0

(h-4)(h-7)=0

h=4 or 7

If the centre of the circle is C(4,3)⇒(x-4)2+(y-3)2=9⇒x2+y2-8x-6y+16=0

If the centre is C(7,6)⇒(x-7)2+(y-6)2=9⇒x2+y2-14x-12y+76=0

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