Example 3
could x^2+y^2+ax + +=0 represent a circle

Yes it could

Step-by-step explanation:

The equation given is a circle. For an equation to represent equation of a circle, the following conditions must be met

1.) The coefficient of x² and y² must be the same

2) The equation must have a linear function containing x and y like AX and ???Y in the equation above.

Since the equation given conforms with the general of a circle x²+y²+2gx+2fy+c = 0, therefore the equation could represents a circle

∠acb = 8°

step-by-step explanation:

∠xba lies on the circle and is half the measure of the intercepted arc ax

hence

measure of arc ax = 2 × 42° = 84°

∠acb is outside the circle and is

∠acb = (arcab - arcax ), hence

∠acb = 0.5 (100 - 84) = 0.5 × 16° = 8°