Question

4x^2+y^2-48x-4y+48=0 A.)

Answer 1

gropu x with x and y with y and complete the squares

(4x^2-48x)+(y^2-4y)+48=0
4(x^2-12x)+(y^2-4y)+48=0
take 1/2 of b and squaer it and ad negative and positive inside
4(x^2-12x+36-36)+(y^2-4y+4-4)+48=0
factor perfect sqare
4((x-6)^2-36)+((y-2)^2-4)+48=0
distribut
4(x-6)^2-144+(y-2)^2-4+48=0
4(x-6)^2+(y-2)^2-100=0
add 100 both sides
4(x-6)^2+(y-2)^2=100
divide both sides by 100

`((x-6)^2)/(25) + ((y-2)^2)/(100) =1`

`((x-6)^2)/(5^2) + ((y-2)^2)/(10^2) =1`
it is a vertical ellipse with center at (6,2), focci at (6,2+5√3) and (6,2-5√3)
major axises at (6,12) and (6,-8) minor axises at (1,2) and at (11,2)