CircleHard

Question

The equation of circles passing through (3, _6) touching both the axes is

Options

A. x2 + y2 _ 6x + 6y + 9 = 0
B. x2 + y2 + 6x _ 6y + 9 = 0

C. x2 + y2 + 30x _ 30y + 225 = 0 (#oD*) x2 + y2 _ 30x + 30y + 225 = 0

##A#

##S#

Now

(r _ 3)2 + (_r + 6)2 = r2

r2 _ 18r + 45 = 0

Þ r = 3, 15

Hence circle

(x _ 3)2 + (y + 3)2 = 32

x2 + y2 _ 6x + 6y + 9 = 0

(x _ 15)2 + (y + 15)2 = (15)2

Þ x2 + y2 _ 30x + 30y + 225 = 0

D.3_14_80_186_1_1_3

The equation of circles passing through (3, _6) touching both the axes is

(#oA) x2 + y2 _ 6x + 6y + 9 = 0 (#oB) x2 + y2 + 6x _ 6y + 9 = 0

(#oC) x2 + y2 + 30x _ 30y + 225 = 0 (#oD*) x2 + y2 _ 30x + 30y + 225 = 0

Solution

Now

(r _ 3)2 + (_r + 6)2 = r2

r2 _ 18r + 45 = 0

Þ r = 3, 15

Hence circle

(x _ 3)2 + (y + 3)2 = 32

x2 + y2 _ 6x + 6y + 9 = 0

(x _ 15)2 + (y + 15)2 = (15)2

Þ x2 + y2 _ 30x + 30y + 225 = 0

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