Question

Can anybody help and explain this? (Part a and b)

Answer 1

Explanation:

Part A

Given equation of the circle is,

x² + y² - 4x + 2y = b

Standard equation of the circle is given by,

(x - h)² + (y - k)² = r²

Here, (h, k) is the center and r = radius of the circle

Now we will convert this equation into a standard equation of the circle,

x² - 4x + y² + 2y = b

x² - 2(2x) + 2² + y² + 2y + 1² = b + 2² + 1²

(x² - 2(2x) + 4) + (y² + 2y + 1) = b + 4 + 1

(x - 2)² + (y + 1)² = √(b + 5)²

Therefore, (2, -1) will be the center of the given circle.

y-coordinate of the circle = -1

Part B

Since, radius of the circle is 7 units,

Therefore,
`√(b+5)=7`

b + 5 = 49

b = 49 - 5

b = 44