Question

What’s the correct answer for this?

Answer 1

Answer:

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

Step-by-step 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