1
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
- 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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