Question

HELP QUICKLY!!!!!!

A circle with equation (x + 2 )2 + (y – 3 )2 = 16 is graphed on the coordinate plane. Which represents the line of tangency at the point (–6, 3)?

A. y = –6

B. x = –6

C. x = 4

D. x = 6

Answer 1

The line of tangency at the point (-6, 3) on the circle is represented by the equation y = 3.

Step-by-step explanation:

The equation of the circle is given by (x + 2)² + (y - 3)² = 16.

To find the line of tangency at the point (-6, 3), we can determine the slope of the line connecting the center of the circle to the point of tangency, which is perpendicular to the tangent line. The center of the circle is (-2, 3), so the slope of the line connecting the center to the point (-6, 3) is m = (3 - 3) / (-6 - (-2)) = 0.

Since a line with slope 0 is a horizontal line, the line of tangency at the point (-6, 3) is represented by the equation y = 3.