Answer:
a) 5
Step-by-step explanation:
2x² - 6x + 2y² + 2y = 45
Complete the square and get it in the form (x-a)² + (y -b)² = r²
2x² - 6x + 2y² + 2y = 45
Divide the equation by 2
x² - 3x + y² + y = 45/2
x² - 3x + ? + y² + y + ?? = 45/2
? -----> (x coefficient by 2)² = (3/2)² = 9/4
?? ----> (y coefficient by 2)² = (1/2)² = 1/4
Add (9/4) & (1/4) to both sides,
x² -3x +(9/4) + y² + y + (1/4) = (45/2)+ (9/4) + (1/4)
(x - 3/2)² + (y + 1/2)² = (90/4) + (9/4) + (1/4)
[tex](x-\frac{3}{2})^{2}+(y+\frac{1}{2})^{2}=\frac{90+9+1}{4}\\\\\\(x-\frac{3}{2})^{2}+(y+\frac{1}{2})^{2}=\frac{100}{4}\\\\\\(x-\frac{3}{2})^{2}+(y+\frac{1}{2})^{2}=25\\\\(x-\frac{3}{2})^{2}+(y+\frac{1}{2})^{2}=5^{2}[/tex]
Radius = 5
