The general form of the equation of a circle is,
x² + y² + Dx + Ey + F = 0, where D, E, F are constants.
The given equation is 7x² + 7y² − 28x + 42y − 35 = 0. So, to convert this equation into a general form we just need to get rid of the leading coefficient 7.
Hence, divide both sides of the equation by 7. So,
[tex] \frac{7x^2+ 7y^2-28x + 42y-35}{7} =0 [/tex]
x² + y² − 4x + 6y − 5=0.
So, the general form of the equation is x² + y² − 4x + 6y − 5=0.
Answer:
The general form of the equation of a circle is
7x2 + 7y2 − 28x + 42y − 35 = 0.
The equation of this circle in standard form is
(x - 2)^2 + (y + 3)^2 = 18
. The center of the circle is at the point
(2, -3)
, and its radius is
3(2^(1/2))
units.
Step-by-step explanation:
1st box - (x - 2)^2 + (y + 3)^2 = 18
2nd box - (2, -3)
3rd box - 3(2^(1/2))
