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

GIVEN: r = 5

c(2,3)

centre lie on x-axis

i.e c(a,0)

A.T.Q

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 ---------------ans

And a= -2

x2 + y2 + 4X -21 =0 -----------------ans

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For ellipse 3x^2+2y^2=6, find the length of major and minor axis, coordinates of focus and vertices and eccentricity
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