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Question

Find the equation of the circle with radius 5 whose centre lies on x-axis and passes through the point (2,3).

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Solution

  • Equation of a circle with centre (h,k) and radius r is given as
  • (x−h)^2+(y−k)^2=r^2

GIVEN: r = 5

c(2,3)

centre lie on x-axis i.e c(a,0)

eq. (2-h)2 + (3-k)2 = 25 ----------------(1)

= (2-a)2 + y2 =25 -----------------------(2)

= 4 - 4a + a2 = 25

= a2 - 4a - 21 =0

= (a-6) (a + 2) =0

therefore a=6 or a= -2

hence

eq. a=6

x2 + y2 - 12x + 11= 0

And a= -2

x2 + y2 + 4X -21 =0






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