Question

What’s the correct answer for this?

Answer 1

a) the co-ordinates of the center are (-3,4) and the length of the radius is 10 units

Center (h,k) = (-3 ,4) and radius 'r' = 10

Explanation:

Step(i):-

Given circle equation is

`2 x^(2) +12 x+2 y^(2) -16 y-150 =0`

Dividing "2' on both sides, we get

`x^(2) +6 x+ y^(2) -8 y-75 =0`

Step(ii):-

now

`x^(2) +2(3x) + (3)^(2)-(3)^(2) +y^(2) -2 (4 y)+(4)^(2)-(4)^2 -75 =0`

by using (a+b)² =a²+2 a b+b²

(a-b)² =a²-2 a b+b²

`(x+3)^(2)-(3)^(2) +(y-4)^(2)-(4)^2 -75 =0`

`(x+3)^(2)-9 +(y-4)^(2)-16 -75 =0`

`(x+3)^(2) +(y-4)^(2)-100 =0`

`(x+3)^(2) +(y-4)^(2)=100`

`(x+3)^(2) +(y-4)^(2)=(10^2)`

by comparing

`(x-h)^(2) +(y-k)^(2)=(r^2)`

Final answer:-

Center (h,k) = (-3 ,4) and radius 'r' = 10