Question

What is the radius of a circle whose equation is x2 y2â’10x 6y 18=0? 2 units 4 units 8 units 16 units.

Answer 1

The radius of the circle is 4 units.

Given to us:

$x^2 + y^2 - 10x + 6y + 18 = 0$

The generalized format for radius of a circle is given by:

$\\(x - h)^2 + (x - k)^2 = a^2\\where,\\h, k= coordinate\ of\ the\ center\ of\ the\ circle\\a= radius\ of\ the\ circle$

therefore after rearrangement of the equation we get,

$x^2 + y^2 - 10x + 6y + 18 = 0,\\x^2 - 10x + y^2 + 6y =- 18,$

adding 25 and 9 on both the sides to bring it in the generalized format for radius of a circle,we get

$x^2 - 10x+25 + y^2+ 6y+9 =-18+25+9,$

$(x - 5)^2 + (y + 3)^2 = 16\\(x - 5)^2 + (y + 3)^2 = 4^2$

Hence, the coordinate for this circle are x=5 and y=-3. And the radius of the circle is 4 units.

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