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Identify the centre and radius of the circle with the given equation and radius of the circle with the given equation: 6x²+6y²+36x-48y-315=0
Answers
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Answer:
center = (-3,4) and radius = 8.8 (approx)
Step-by-step explanation:
6x²+6y²+36x-48y-315=0
Firstly, group like terms
(6x²+36x) + (6y²-48y) = 315
Then complete the square
(6x² + 36x + 54) + (6y² - 48 + 96) = 315 + 54 + 96
In LHS factor 6 from each grouped term and in RHS add the numbers
6( x² + 6x + 9 ) + 6( y² - 8y + 16 ) = 465
6(x + 3)² + 6( y - 4 )² = 465
Divide both sides by 6
( x + 3 )² + ( y - 4 )² = 465/6
Compare with Equation of circle
( x - h )² + ( y - k )² = r² (here (h,k) is the center and r is the radius)
On comparing,
( -3, 4 ) is the center
square root of 465/6 or 8.8 is the radius