True or False:
•Every equation of the form
X^2+y^2+ax+by+c=c
•The radius of the circle
x^2+y^2=9 is 3
•The center of the circle
(X+3)^2+(y-2)^2=13 is (3,-2)
I do not know what the first one is supposed to be, either a typo or totally false
The second is true
the third has the signs backwards, should be (-3 ,2)
Looks like the first one is intended to be the equation of a circle.
(x^2 + ax) + (y^2 + by) = 0
Unfortunately, if a or b is not zero, there is no real graph.
If a=b=0, then the graph is just the point (0,0).
If there was a typo, giving a "d" on the right-hand side, then given suitable a,b,c,d there will be a circle that satisfies the equation.
Oh yes the first one was a typo it was supposed to be X^2+y^2+ax+by+c=0
• False: The given equation X^2+y^2+ax+by+c=c is not an equation of a circle. The equation of a circle is usually in the form (x-h)^2 + (y-k)^2 = r^2, where (h, k) represents the center of the circle, and r represents the radius. The equation provided does not follow this form.
• True: The equation x^2+y^2=9 represents a circle with a radius of 3. In this equation, the radius is represented by the number on the right side of the equation after the equal sign. Since 3^2 = 9, the radius is indeed 3.
• False: The center of the circle (X+3)^2+(y-2)^2=13 is not (3,-2). In the equation, the terms (X+3) and (y-2) indicate the displacement of the center from the origin. Thus, the center of the circle is located at the point (-3, 2) rather than (3,-2).