For the given circles $x^{2} + y^{2} - 6 x - 2 y + 1 = 0$ and $x^{2} + y^{2} + 2 x - 8 y + 13 = 0$ , which of the following is true

One circle lies inside the other

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One circle lies completely outside the other

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Two circle intersect in two points

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They touch each other

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Solution

The correct option is D
They touch each other

$C_{1} (3, 1), r_{1} = \sqrt{9 + 1 - 1}, r_{1} = 3 C_{2} (- 1, 4), r_{2} = \sqrt{1 + 16 - 13} = 2 C_{1} C_{2} = \sqrt{16 + 9} = 5 C_{1} C_{2} = r_{1} + r_{2}$

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For the given circles x2+y2−6x−2y+1=0 and x2+y2+2x−8y+13=0, which of the following is true

The correct option is D They touch each other C1(3,1),r1=√9+1−1,r1=3C2(−1,4),r2=√1+16−13=2C1C2=√16+9=5C1C2=r1+r2

For the given circles $x^{2} + y^{2} - 6 x - 2 y + 1 = 0$ and $x^{2} + y^{2} + 2 x - 8 y + 13 = 0$ , which of the following is true

The correct option is D
They touch each other

$C_{1} (3, 1), r_{1} = \sqrt{9 + 1 - 1}, r_{1} = 3 C_{2} (- 1, 4), r_{2} = \sqrt{1 + 16 - 13} = 2 C_{1} C_{2} = \sqrt{16 + 9} = 5 C_{1} C_{2} = r_{1} + r_{2}$