What is an equation for the translation of (x-2)^2+(y+1)^2=16

Asked by maham237 @ 25/12/2020 in Mathematics viewed by 313 People

by 3 units left

Answered by maham237 @ 25/12/2020

Answer: ( x + 1)² + (y - 4)² = 16

Explanation:

1) The given equation, ( x - 2)² + (y + 1)² = 16, represents a circumference with center (2,-1) and radius √16 = 4.

1) The translation will not modify the radius of the circunference, siince translations are rigid transformations.

2) The translation 3 units to the left and 5 units upward certainly will move the center of the circunference.

This is how:

(x,y) → (x - 3, y + 5)

(2, -1) → (2 - 3, - 1 + 5) = (- 1, 4)

3) Then, keeping the same radius and being the center (-1,4), the equation of the circumference after the translation will be:

( x + 1)² + (y - 4)² = 16 ← answer

What is an equation for the translation of (x-2)^2+(y+1)^2=16

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