Answer :
Answer:
The standard form of a circle is (x-h)^2 + (y-k)^2 = r^2 with (h,k) being the center of the circle and r being the radius. In this case the circle's equation in standard form is (x-2)^2 + (y+3)^2 = 18. Knowing this it's easy to see that the center of the circle (h,k) is (2,-3). Finally the radius is [tex]\sqrt{18}[/tex] or in simplified terms, 3[tex]\sqrt{2}[/tex]
Step-by-step explanation:
Answer:
see explanation
Step-by-step explanation:
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r is the radius
Given
7x² + 7y² - 28x + 42y - 35 = 0 ( divide through by 7 )
x² + y² - 4x + 6y - 5 = 0
Collect x- terms and y- terms together and add 5 to both sides
x² - 4x + y² + 6y = 5
Use the method of completing the square to obtain standard form
add ( half the coefficient of the x / y term)² to both sides
x² + 2(- 2)x + 4 + y² + 2(3)y + 9 = 5 + 4 + 9
(x - 2)² + (y + 3)² = 18 ← in standard form
here (h, k) = (- 2, 3) and r = [tex]\sqrt{18}[/tex] = 3[tex]\sqrt{2}[/tex]
Centre = (2, - 3) and radius = 3[tex]\sqrt{2}[/tex]
