Question

Complete the following: 1, Jabomplete the squares for each quadratic, list the center and radius, then graph each circle (a labeling its translated center: (a) r2 + 2x + y2 - 4y = 4 (c) 2x2 + 2y2 + 3x - 5y = 2 (e) r2 + y2 + 3x = 4 (g) x² + y2 + 4x = 0 (1) r² + y2 + 2mx - 2ny = 0 (b) x2 + y2 - 4x = 0 (d) x2 + y2 - 2x - 8y = 8 4x + 4y? - 16x + 24y = -27 (h) x + y? - 7y = 0 (i) x + y2 - 2ax + 2by = c Determine which of the following equations represents a circle with a real non-zero radiu a) r? + y + 10x = -30 (b) 3x2 + 3y? - 11x = -91 4x + 4y + 18-8y = -85 (d) 36x* + 36y- 36x + 48y = -16 the equation of the circle which accen 2 and is concentric

Answer 1

3x² + 3y² - 11x = -91

Divide through by 3

x² + y² - 11/3 x = -91/3

x² - 11/3 x + y² = -91/3

(x² - 11/3 x ) + y² = -91/3

[x² - 11/3 x +(-11/6)² ] + y² = -91/3 + (- 11/6)²

(x - 11/6)² + y² = -91/3 + 121 / 36

`(x-(11)/(6))^2+y^2=\frac{-1092+\text{ 121}}{36}`

`(x\text{ - }(11)/(6))^2+y^2=(-971)/(36)`

Comparing this with (x-a)² + (y-b)² = r²

r² = -971/36

Taking the square root will give an immaginary number

The radius is NOT a real number

This equation does not have a real radius