Question

Really need help guys!
Love you if you can solve them wiz steps!!!!

Answer 1

Explanation:

`x^2+y^2-8x+4y+4=0\\\\a)\\\\x^2-8x+y^2+4y+4=0\\\\x^2-2*x*4+(y^2+2*y*2+2^2)=0\\\\x^2-2*x*4+4^2+(y+2)^2=4^2\\\\(x-4)^2+(y+2)^2=4^2\\`

Hence,

The radius of the circle is 4 units, coordinates of its centre are (4,-2).

`b)\\\\y=0\\x^2+0^2-8x+4*0+4=0\\x^2-8x+4=0\\a=1\ \ \ \ b=-8\ \ \ \ c=4\\D=(-8)^2-4*1*4\\D=64-14\\D=48\\√(D)=√(48) \\ √(D)=√(16*3) \\√(D)=√(4^2*3) \\√(D)=4√(3) \\\displaystyle\\x=(-(-8)б4√(3) )/(2*1) \\\\x=(8б4√(3) )/(2) \\x_1=4-2√(3) \\x_2=4+2√(3)`

`c)\\\\A(6,2√(3)-2)\\ (x-4)^2+(y+2)^2=4^2\\(6-4)^2+(2√(3) -2+2)^2=16\\2^2+(2√(3) )^2=16\\4+2^2*(√(3))^2=16\\ 4+4*3=16\\4+12=16\\16\equiv16`

`d)\\A(6,2√(3)-2)}\\√(3) x+3y=\\√(3)(6)+3(2√(3) -2)=\\ 6√(3)+6√(3) -6=\\ 12√(3)-6`