Question

The image shows the graph of `\left(x-5\right)^{2} \left(y 1\right)^{2}=25` Find and verify at least one point where the circle and line intersect.

Answer 1

Substituting y = x - 5 into the equation of the circle, we get:                         (x - 5)² + (x - 4)² = 25.                                                                                                Expanding and simplifying, we get:                                                                         2x² - 18x + 16 = 0(x-1)(x-8) = 0x = 1   or   x = 8                                                      Therefore, the line intersects the circle at two points:                                         (1, -4) and (8, 3).

*WARNING

This is under the assumption that this is the equation given:

(x - 5)2 + (y + 1)² = 25.