Respuesta :
Answer:
Centre = ( - 4, - 5 )
Radius = 7
Step-by-step explanation:
x² + y² + 8x + 10y - 8 = 0
It is in the form of x² + y² + 2gx + 2fy + c = 0 ( General circle equation ).
where,
2g = 8
g = 4
2f = 10
f = 5
c = - 8
Formula : -
The centre of the circle = ( - g, - f )
So,
The centre of the circle is ( - 4, - 5 ).
Formula : -
( Radius )² = g² + f² - c
( Radius )² = ( - 4 )² + ( - 5 )² - ( - 8 )
= 16 + 25 + 8
( Radius )² = 49
Square root on both sides,
Radius = √49 = 7
Answer:
See below ~
Step-by-step explanation:
Given
- x² + y² + 8x + 10y - 8 = 0
Completing the square method (for both x and y)
- Add and subtract 16 and 25.
- x² + 8x + 16 - 16 + y² + 10y + 25 - 25 - 8 = 0
- (x + 4)² + (y + 5)² - 49 = 0
2. Bring the constant term to the other side by adding 49 on both sides.
- (x + 4)² + (y + 5)² - 49 + 49 = 0 + 49
- (x + 4)² + (y + 5)² = 49
3. Centre = (x, y)
- x + 4 = 0
- x = -4
- y + 5 = 0
- y = -5
- Centre = (-4, -5)
4. Radius
- r² = 49
- r = √49
- radius = 7
