The equation of circle a is x2 + y2 + cx + dy + e = 0. if the circle is moved horizontally to the left of the y-axis without changing the radius, how are the coefficients c and d affected?

You can complete the square to find the equation of the circle in standard form.







So the circle is centered at and has radius .

A horizontal shift to the left can be done by adding a positive number to the term, as in



Expanding, you end up with



So the coefficient is increased by twice the horizontal shift, while remains unchanged.

Ithink if ur looking for a ratio it would be 12: 3