Question

What does the equation (x – a)² + (y – b)² = r² become when the axes are transferred to parallel axes through the point (a - c, b)?

Answer 1

Given:

The equation, (x – a) ² + (y – b) ² = r² 

The given equation (x – a)² + (y – b)² = r² can be transformed into the new equation by changing x by x – a + c and y by y – b, i.e. substitution of x by x + a and y by y + b.

((x + a – c) – a)² + ((y – b ) – b)² = r²

(x – c)² + y² = r²

x² + c² – 2cx + y² = r²

x² + y² -2cx = r² – c² 

Hence, the transformed equation is x² + y² -2cx = r² – c²