Q. 134.4( 11 Votes )

Find the eq

Answer :

Given that we need to find the equations of the circles passing through the points on y - axis at distances 3 from origin and having radius 5.



Since the points are 3 units away from origin on the y - axis, the points will be (0,3) and (0, - 3).


Let us assume the centre of this circle be (h,k).


We know that the equation of the circle with centre (p,q) and having radius ‘r’ is given by:


(x - p)2 + (y - q)2 = r2


Now we substitute the corresponding values in the equation:


(x - h)2 + (y - k)2 = 52


(x - h)2 + (y - k)2 = 25 ..... (1)


Since circle passes through the point (0,3). We substitute this point in eq(1)


(0 - h)2 + (3 - k)2 = 25


h2 + (3 - k)2 = 25 ..... - - (2)


Since circle passes through the point (0, - 3). We substitute this point in eq(1)


(0 - h)2 + ( - 3 - k)2 = 25


h2 + (3 + k)2 = 25 ..... - - (3)


On solving (2) and (3), we get


h = ±4 and k = 0


We have circle with centre (±4,0) and having radius 5 units.


We know that the equation of the circle with centre (p, q) and having radius ‘r’ is given by:


(x - p)2 + (y - q)2 = r2


Now we substitute the corresponding values in the equation:


(x±4)2 + (y - 0)2 = 52


x2±8x + 16 + y2 = 25


x2 + y2±8x - 9 = 0


The equations of the circles is x2 + y2±8x - 9 = 0.


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