The radius of the circle of least size that passes through $(- 2, 1)$ and touches both axes is?

1

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Solution

The correct option is B $1$
Equation of the circle $(x - h)^{2} + (y - h)^{2} = h^{2}$
$x^{2} - 2 h x + h^{2} + y^{2} - 2 h y + h^{2} = h^{2}$
$4 + 4 h + h^{2} + 1 - 2 h = 0$
$h^{2} + 2 h + 5 = 0$
Minimum value $2 h + 2 = 0$
$h = - 1$
Radius, $| h | = 1$

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The radius of the circle of least size that passes through (−2,1) and touches both axes is?

The correct option is B 1Equation of the circle (x−h)2+(y−h)2=h2x2−2hx+h2+y2−2hy+h2=h24+4h+h2+1−2h=0h2+2h+5=0Minimum value 2h+2=0h=−1Radius, |h|=1

The radius of the circle of least size that passes through $(- 2, 1)$ and touches both axes is?

The correct option is B $1$
Equation of the circle $(x - h)^{2} + (y - h)^{2} = h^{2}$
$x^{2} - 2 h x + h^{2} + y^{2} - 2 h y + h^{2} = h^{2}$
$4 + 4 h + h^{2} + 1 - 2 h = 0$
$h^{2} + 2 h + 5 = 0$
Minimum value $2 h + 2 = 0$
$h = - 1$
Radius, $| h | = 1$