Question

the equation of circle A is x^2+y^2+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

Answer 1

When the circle A moves horizontally to left of y-axis, it changes the value of C in the equation.

Explanation:

Given is the equation of a circle A as follows:-

x^2+y^2+Cx+Dy+E=0

We see the coefficients of x^2 and y^2 terms are 1 each. It means we can find the center of the circle from the equation itself as follows:-

Coordinates of center of circle A: (-C/2 , -D/2)

When they move the circle horizontally to the left of the y-axis, without changing its radius, the x-coordinate of the center (i.e. -c/2) in the circle A will change accordingly. And y-coordinate remains unchanged.

So when we move the circle horizontally to the left of y-axis, it changes the value of C in the equation of circle.