The generic version of the circle equation is, x² + y² + 16x - 8y + 73 = 0.
Definition of circle:
A circle is a closed two-dimensional object in which all points in the plane are equidistant from a single point known as the "centre." The line of reflection symmetry is formed by every line that travels through the circle. For any angle, it also exhibits rotational symmetry around the center.
Step-by-step:
Step 1:
The conventional form of the circle equation is expressed as:
(x - a)² + (y - b)² = r²
where centers are specified as (a,b)
The circle equation given in the question is:
x² + y² = 7
If the circle is translated T(-8,4), the center of the translated circle is located at (-8,4).
As a result, the conventional version of the circle equation is:
(x + 8) ² + (y - 4) ² = 7
Step 2:
Simplifying the problem:
(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 generic version of the circle equation.
Learn more about equation of circle here, https://brainly.com/question/1506955
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