Complete the square and then find the center and radius from the circle equation
2 answers:
Answer:
center: (2, -4); radius: 5
Step-by-step explanation:
Group x-terms and y-terms. Add the squares of half the coefficient of the linear term in each group. It can be convenient to subtract the constant, too.
(x^2 -4x) +(y^2 +8y) = 5
(x^2 -4x +4) +(y^2 +8x +16) = 5 + 4 + 16
(x -2)^2 +(y +4)^2 = 5^2
Comparing this to the form of a circle centered at (h, k) with radius r, we can find the center and radius.
(x -h)^2 +(y -k)^2 = r^2
(h, k) = (2, -4) . . . . . the circle center
r = 5 . . . . . . . . . . . . the radius
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a. We can find all of these length using the cosine of the angle, Pythagoras theorem and the principle of the similarity of triangles.
b. According to the cosine of the angle we can write that, cosθ = 12/a = 5/13 and from here a = 31.2. After finding that using Pythagoras theorem, we can write that . According to the similarity of the triangles, we can write that 31.2/d = 28.8/12 and d = 13. Applying Pythagoras theorem we find that c = 5.
c. We already gave the answer for this question in part b