Find the intercepts of the circle. Round to the nearest hundredth, when necessary.
-$$( x + 4 ) ^ { 2 } + ( y - 2 ) ^ { 2 } = 28$$
A)The two x-intercepts are x ≈8.9 and x ≈-0.9, and the two y-intercepts are y ≈1.46 and y ≈-5.46.
B)The two x-intercepts are x ≈0.9 and x ≈-8.9, and the two y-intercepts are y ≈5.46 and y ≈-1.46.
C)There are no intercepts.
D)The two x-intercepts are x ≈1.66 and x ≈-9.66, and the two y-intercepts are y ≈8.63 and y ≈-4.63.

Question

Quizplus · Accepted Answer

To find the x-intercepts, set y=0 and solve for x: $(x+4)^2 + (2)^2 = 28$, which simplifies to $x^2 + 8x - 24 = 0$. Solving this quadratic equation gives $x \approx 0.9$ and $x \approx -8.9$. For the y-intercepts, set x=0 and solve for y: $(4)^2 + (y-2)^2 = 28$, leading to $y^2 - 4y - 20 = 0$. Solving gives $y \approx 5.46$ and $y \approx -1.46$.

Find the Intercepts of the Circle (x+4)2+(y−2)2=28( x + 4 ) ^ { 2 } + ( y - 2 ) ^ { 2 } = 28(x+4)2+(y−2)2=28

Find the Intercepts of the Circle $( x + 4 ) ^ { 2 } + ( y - 2 ) ^ { 2 } = 28$