Answer:
(x + 2)² + (y + 1)² = 9
Step-by-step explanation:
Gina started with a circle with the given equation as,
(x - 2)² + (y - 0)² = 16
Since, standard equation of a circle is,
(x - a)² + (y - b)² = r²
Here (a, b) is the center of the circle and 'r' is the radius.
Therefore, from the given equation of the circle,
Center of the circle → (2, 0)
Radius of the circle → √16 = 4 units
She translated this circle 4 units left and 1 unit down.
Rule for the new center after translation will be,
(x, y) → (x - 4, y - 1)
(2, 0) → (2 - 4, 0 - 1)
→ (-2, -1)
Coordinates of the new center → (-2, -1)
Then she reduced the radius by 1 units.
Therefore, radius of the new circle = 4 - 1 = 3 units
Now we substitute these values in the standard equation of the circle to get the equation of the new circle.
(x + 2)² + (y + 1)² = 3²
(x + 2)² + (y + 1)² = 9
