QuestionThe line $x+5 y+22=0$ intersects the circle $x^{2}+y^{2}+4 x+8 y-6=0$ at the point $A$ and $B$. Find the coordinates of $A$ and $B$. Answer a. $A(7,-3), B(3,5)$ b. $A(7,-3), B(3,-5)$ c. $A(6,-3), B(3,-7)$ d. $A(6,-3), B(3,-7)$

Studdy Solution
Verify the points $(-7, -3)$ and $(3, -5)$ by substituting them back into the circle equation.
For $(-7, -3)$:
$$(-7)^2 + (-3)^2 + 4(-7) + 8(-3) - 6 = 49 + 9 - 28 - 24 - 6 = 0$$
For $(3, -5)$:
$$(3)^2 + (-5)^2 + 4(3) + 8(-5) - 6 = 9 + 25 + 12 - 40 - 6 = 0$$
Both points satisfy the circle equation.
The coordinates of points $A$ and $B$ are:
$$A(-7, -3) \text{ and } B(3, -5)$$
Therefore, the correct answer is not among the given options indicating a miscalculation or a typo in the options. The correct points should be:
$$A(-7, -3) \text{ and } B(3, -5)$$