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For the given circles $5 x^{2} + y^{2} - 6 x - 2 y + 1 = 0$ and $x^{2} + y^{2} + 2 x - 8 y + 13 = 0$ which of the following is true?

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One circle lies inside the other

One circle lies completely outside the other

Two circles intersection in two points

They touch each other externally

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detailed solution

Correct option is D

The centres of the given circles are C1(3,1) and C2(−1,4) and corresponding radii are r1=32+12−1=3and r=(−1)2+42−13=2 respectively.Now C1C2=(3+1)2+(1−4)2=5Clearly, C1C2=(3+1)2+(1−4)2=5So, given circles touch each other externally.

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For the given circles 5x2+y2−6x−2y+1=0 and x2+y2+2x−8y+13=0 which of the following is true?

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material

For the given circles $5 x^{2} + y^{2} - 6 x - 2 y + 1 = 0$ and $x^{2} + y^{2} + 2 x - 8 y + 13 = 0$ which of the following is true?