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The equation of a circle is x^2+y^2-4 x+8 y+20=0 . Determine the nature of the circle.

 

Option: 1

Real Circle

 


Option: 2

Imaginary Circle

 


Option: 3

Point Circle

 


Option: 4

None of the above


Answers (1)

best_answer

Comparing the given equation with the standard equation of a circle, we get:

\begin{aligned} &2 g=-4,2 f=8, c=20\\ &g^2+f^2-c=(-2)^2+4^2-20=4+16-20=0 \end{aligned}

Since g^2+f^2-c=0 the radius of the circle is real and equal to 0. Therefore, the given circle is a point circle.

 

Posted by

vishal kumar

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