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Which of these is NOT a real circle ? 

Option: 1

x^2 + y^2 +6x + 6y + 6 = 0


Option: 2

x^2 + y^2 -6x + 10 y +36 = 0


Option: 3

x^2 + y^2 + 100 x + 100 y + 10000 = 0


Option: 4

(b)  and  (c)


Answers (1)

best_answer

As we have learned

Real Circle -

g^{2}+f^{2}-c> 0

 

- wherein

The equation of circle is x^{2}+y^{2}+2gx+2fy+c= 0 .
 

for circle: x^2 + y^2 +6x + 6y + 6 = 0

g^2 + f^2 - c = 3^2 + 3^2 - 3 = 15 > 0

for circle: x^2 + y^2 -6x + 10 y +36 = 0

g^{2}+f^{2}-c = 3^2 + 5^2 - 36 = 0

for circle; x^2 + y^2 + 100 x + 100 y + 10000 = 0

  g^{2}+f^{2}-c = 50 ^2 + 50 ^2 - 10000 \\ = 5000 - 10000 < 0

Hence, Options (c).

 

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seema garhwal

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