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The circles x2+y2+6x+6y = 0 and x2+y2−12x−12y = 0
- a)touch each other externally
- b)touch each other internally
- c)cut orthogonally
- d)intersect in two points
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
The circlesx2+y2+6x+6y = 0 andx2+y2−12x−12y = 0a)touch eac...
Given equation of circles are
x2+y2+6x+6y=0....(i)
and x2+y2−12x−12y=0....(ii)
Here, g1 = 3,f2 = 3, g2 = −6 and f2 = −6
∴ Centres of circles are C1(−3,−3) and C2(6,6) respectively and radii are r1 = 3√2 and r2 = 6√2 respectively.
Now, C1C2 = √[(6+3)2 + (6+3)2]
= 9√2
and r1 + r2
= 3(2)1/2 + 6(2)1/2
= 9(2)1/2
⇒ C1C2 = r1 + r2
∴ Both circles touch each other externally.
x2+y2+6x+6y=0....(i)
and x2+y2−12x−12y=0....(ii)
Here, g1 = 3,f2 = 3, g2 = −6 and f2 = −6
∴ Centres of circles are C1(−3,−3) and C2(6,6) respectively and radii are r1 = 3√2 and r2 = 6√2 respectively.
Now, C1C2 = √[(6+3)2 + (6+3)2]
= 9√2
and r1 + r2
= 3(2)1/2 + 6(2)1/2
= 9(2)1/2
⇒ C1C2 = r1 + r2
∴ Both circles touch each other externally.
Most Upvoted Answer
The circlesx2+y2+6x+6y = 0 andx2+y2−12x−12y = 0a)touch eac...
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The circlesx2+y2+6x+6y = 0 andx2+y2−12x−12y = 0a)touch each other externallyb)touch each other internallyc)cut orthogonallyd)intersect in two pointsCorrect answer is option 'A'. Can you explain this answer?
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