Question

A circle has radius equal to 3 units and its centre lies on the line y = x – 1. Find the equation of the circle if it passes through (7, 3)
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Answer 1

(x−h)

(x−h) 2

(x−h) 2 +(y−k)

(x−h) 2 +(y−k) 2

(x−h) 2 +(y−k) 2 =r

(x−h) 2 +(y−k) 2 =r 2

(x−h) 2 +(y−k) 2 =r 2

(x−h) 2 +(y−k) 2 =r 2 Here (h,k)→ centre

(x−h) 2 +(y−k) 2 =r 2 Here (h,k)→ centreEquation of line through centre

(x−h) 2 +(y−k) 2 =r 2 Here (h,k)→ centreEquation of line through centre k=h−1−−−−(1)w

& (x,y) point on circle

& (x,y) point on circleSo, given (x,y)=(7,3)

& (x,y) point on circleSo, given (x,y)=(7,3)So, (7−h)

& (x,y) point on circleSo, given (x,y)=(7,3)So, (7−h) 2

& (x,y) point on circleSo, given (x,y)=(7,3)So, (7−h) 2 +(3−h+1)

& (x,y) point on circleSo, given (x,y)=(7,3)So, (7−h) 2 +(3−h+1) 2

& (x,y) point on circleSo, given (x,y)=(7,3)So, (7−h) 2 +(3−h+1) 2 =3

& (x,y) point on circleSo, given (x,y)=(7,3)So, (7−h) 2 +(3−h+1) 2 =3 2

& (x,y) point on circleSo, given (x,y)=(7,3)So, (7−h) 2 +(3−h+1) 2 =3 2

& (x,y) point on circleSo, given (x,y)=(7,3)So, (7−h) 2 +(3−h+1) 2 =3 2 Using eqn (1)

& (x,y) point on circleSo, given (x,y)=(7,3)So, (7−h) 2 +(3−h+1) 2 =3 2 Using eqn (1)We get,

& (x,y) point on circleSo, given (x,y)=(7,3)So, (7−h) 2 +(3−h+1) 2 =3 2 Using eqn (1)We get,28+h

& (x,y) point on circleSo, given (x,y)=(7,3)So, (7−h) 2 +(3−h+1) 2 =3 2 Using eqn (1)We get,28+h 2

& (x,y) point on circleSo, given (x,y)=(7,3)So, (7−h) 2 +(3−h+1) 2 =3 2 Using eqn (1)We get,28+h 2 −11h=0

& (x,y) point on circleSo, given (x,y)=(7,3)So, (7−h) 2 +(3−h+1) 2 =3 2 Using eqn (1)We get,28+h 2 −11h=0h=7 oR 4

& (x,y) point on circleSo, given (x,y)=(7,3)So, (7−h) 2 +(3−h+1) 2 =3 2 Using eqn (1)We get,28+h 2 −11h=0h=7 oR 4k=6 oR 3

& (x,y) point on circleSo, given (x,y)=(7,3)So, (7−h) 2 +(3−h+1) 2 =3 2 Using eqn (1)We get,28+h 2 −11h=0h=7 oR 4k=6 oR 3Equation of circle corresponding (7,6)

& (x,y) point on circleSo, given (x,y)=(7,3)So, (7−h) 2 +(3−h+1) 2 =3 2 Using eqn (1)We get,28+h 2 −11h=0h=7 oR 4k=6 oR 3Equation of circle corresponding (7,6)x

& (x,y) point on circleSo, given (x,y)=(7,3)So, (7−h) 2 +(3−h+1) 2 =3 2 Using eqn (1)We get,28+h 2 −11h=0h=7 oR 4k=6 oR 3Equation of circle corresponding (7,6)x 2

& (x,y) point on circleSo, given (x,y)=(7,3)So, (7−h) 2 +(3−h+1) 2 =3 2 Using eqn (1)We get,28+h 2 −11h=0h=7 oR 4k=6 oR 3Equation of circle corresponding (7,6)x 2 +y

& (x,y) point on circleSo, given (x,y)=(7,3)So, (7−h) 2 +(3−h+1) 2 =3 2 Using eqn (1)We get,28+h 2 −11h=0h=7 oR 4k=6 oR 3Equation of circle corresponding (7,6)x 2 +y 2

& (x,y) point on circleSo, given (x,y)=(7,3)So, (7−h) 2 +(3−h+1) 2 =3 2 Using eqn (1)We get,28+h 2 −11h=0h=7 oR 4k=6 oR 3Equation of circle corresponding (7,6)x 2 +y 2 −14x−12y+76=0

& (x,y) point on circleSo, given (x,y)=(7,3)So, (7−h) 2 +(3−h+1) 2 =3 2 Using eqn (1)We get,28+h 2 −11h=0h=7 oR 4k=6 oR 3Equation of circle corresponding (7,6)x 2 +y 2 −14x−12y+76=0Equation of circle corresponding (4,3)

& (x,y) point on circleSo, given (x,y)=(7,3)So, (7−h) 2 +(3−h+1) 2 =3 2 Using eqn (1)We get,28+h 2 −11h=0h=7 oR 4k=6 oR 3Equation of circle corresponding (7,6)x 2 +y 2 −14x−12y+76=0Equation of circle corresponding (4,3)x

& (x,y) point on circleSo, given (x,y)=(7,3)So, (7−h) 2 +(3−h+1) 2 =3 2 Using eqn (1)We get,28+h 2 −11h=0h=7 oR 4k=6 oR 3Equation of circle corresponding (7,6)x 2 +y 2 −14x−12y+76=0Equation of circle corresponding (4,3)x 2

& (x,y) point on circleSo, given (x,y)=(7,3)So, (7−h) 2 +(3−h+1) 2 =3 2 Using eqn (1)We get,28+h 2 −11h=0h=7 oR 4k=6 oR 3Equation of circle corresponding (7,6)x 2 +y 2 −14x−12y+76=0Equation of circle corresponding (4,3)x 2 +y

& (x,y) point on circleSo, given (x,y)=(7,3)So, (7−h) 2 +(3−h+1) 2 =3 2 Using eqn (1)We get,28+h 2 −11h=0h=7 oR 4k=6 oR 3Equation of circle corresponding (7,6)x 2 +y 2 −14x−12y+76=0Equation of circle corresponding (4,3)x 2 +y 2

& (x,y) point on circleSo, given (x,y)=(7,3)So, (7−h) 2 +(3−h+1) 2 =3 2 Using eqn (1)We get,28+h 2 −11h=0h=7 oR 4k=6 oR 3Equation of circle corresponding (7,6)x 2 +y 2 −14x−12y+76=0Equation of circle corresponding (4,3)x 2 +y 2 −8x−6y+16=0

Answer 2

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