Mth101 first assignment spring 2011 solution

[sana.pari]

Question # 2
4x2+4y2+16y-4x=19
4x2+4y2+2(-2)x+2(4y)-19=0
g = -2
f = +8 c = -19
r = f 2 + g2 − c
= (−2)2 + 82 − (−19)
= 4 + 64 + 19
= 87
Radius = 87
Center = (-2, 8)

Question # 3
x ≥ −2
8 − x
⇒ x ≥ −2 ( 8 − x )
⇒ x ≥ −16 + 2 x
⇒ x − 2 x ≥ −16
⇒ − x ≥ −16
⇒ x ≤ 16
⇒ { x x ∈ R x ≤ 16}