Identify the equation of the translated graph in general form x^2+y^2=7 for T (-8,4) A. x^2 + y^2 + 16x - 8y + 73 = 0 B. x^2 + y^2 + 8x - 4y - 73 = 0 C. x^2 + y^2 + 16x + 8y + 73 = 0 D. x^2 + y^2 + 8x + 4y + 73 = 0

The correct option is A

Step-by-step explanation:

The standard form of equation of circle is written as:

(x - a) ² + (y - b) ² = r²

Where centers is given as (a, b)

The equation of the circle given in the question is:

x² + y² = 7

If the circle is translated T (-8,4), it means that the centre of translated circle lies at (-8,4).

So standard form of equation of circle is:

(x + 8) ² + (y - 4) ² = 7

Simplifying the equation:

(x² + 64 + 2 (x) (8)) + (y² + 16 - 2 (y) (4)) = 7

x² + 64 + 16x + y² + 16 - 8y = 7

x² + y² + 16x - 8y + 80 = 7

x² + y² + 16x - 8y + 80 - 7 = 0

x² + y² + 16x - 8y + 73 = 0

which is the general form of the equation of circle