Question

Write the equation in standard form and classify the comic section it defines.

1.
2x^2 - 4y^2 - 16x + 48y -120 = 0

2. 2x^2 + 4y^2 + 20x + 8y + 46 = 0

Answer 1

comlplete the squares for each


gropu x's and y's and solve



remember completeing square? do tat for x's and y's

so

(2x²-16x)+(-4y²+48y)-120=0
2(x²-8x)-4(y²-12y)-120=0
2(x²-8x+16-16)-4(y²-12y+36-36)-120=0
2((x-4)²-16)-4((y-6)²-36)-120=0
2(x-4)²-32-4(y-6)²+144-120=0
2(x-4)²-4(y-6)²=8
divide both sides by 8

`((x-4)^2)/(4)- ((y-6)^2)/(2)=1`
das be hyperbola








2.
(2x²+20x)+(4y²+8y)+46=0
2(x²+10x)+4(y²+2y)+46=0
2(x²+10x+25-25)+4(y²+2y+1-1)+46=0
2((x+5)²-25)+4((y+1)²-1)+46=0
2(x+5)²-50+4(y+1)²-4+46=0
2(x+5)²+4(y+1)²-8=0
2(x+5)²+4(y+1)²=8
divide by 8

`((x+5)^2)/(4)+ ((y+1)^2)/(2) =1`
das is elipse (becase it is plus)