Question

3. x2 + y2 + 2gx + 2 fy+c=0​

Answer 1

Answer:

it's a equation of circle whose centre coordinate are you (-g, -f) and whose radius is square root(g2+f2-c)

Answer 2

Answer:

Step-by-step explanation:

We know General equation of second degree

ax^2 + by^2 +2hxy +2gx+2fy+c =0…(1) ,

represents a circle when h= 0 & a=b.

And when a=b=1, then the above equation(1) becomes

x^2+y^2+2gx+2fy+c=0,…(2),

if we add g^2 & f^2 on both the side of equation (2) , we get

x^2 + 2gx +g^2 +y^2+2fy+f^2 = g^2+f^2-c

Or, (x+g)^2 +(y+f)^2 ={√(g^2+f^2-c)}^2 ..(3)

Now if we zoom on equation (3) , & compare it with popular form of the equation of circle

(x-h)^2 +(y-k)^2 = r^2 ,

we find that it (equation 3) clearly represents a circle having centre (-g ,-f) & radius √(g^2+f^2-c).

Hopefully we are convinced now……