Find the equation of the circle touching both the axis and whose centre lies 2x ndash 4y 7 ........

Quantitative Aptitude (CDS) Coordinate Geometry

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Find the equation of the circle touching both the axis and whose centre lies 2x – 4y = 7.

(x-7/2)²+(y+7/2)²=(7/2)²

(x+7/6)²+(y+7/6)²=(7/6)²

(x-7/6)²+(y+7/2)²=(7/6)²

(x+7/2)²+(y+7/6)²=1

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Explanation:

lets consider radius r so in 4 quadrant 4 centre (r, r) , (-r, r), (-r, -r) , (r,- r)
on putting these values in line 2x – 4y = 7 we get r = ±7/2 and ±7/6
r > 0 always so only two centre valid
hence two equation formed by these two centre & r = 7/2, 7/6
equation of the circle having centre ( h , k ) & radius r is given by
(x-h)²+(y-k)²=r²
We get ( x-7/6)²+(y+7/2)²=(7/6)²
& (x+7/2)²+(y+7/2)²=(7/2)²