Identify the conic section given by displaystyle{y}^{2}+{2}{y}={4}{x}^{2}+{3} Find its frac{text{vertex}}{text{vertices}} text{and} frac{text{focus}}{text{foci}}

nicekikah 2021-02-10 Answered
Identify the conic section given by y2+2y=4x2+3
Find its vertexvertices and focusfoci
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Expert Answer

unett
Answered 2021-02-11 Author has 119 answers
Step 1
We rewrite the equation as:
y2+2y=4x2+3
y2+2y4x2=3
y2+2y+14x2=3+1
(y+1)24x2=4
(y+1)244x24=1
(y+1)24x21=1
This is an equation of a hyperbola.
Step 2
Then we compare the equation with standard form.
(y+1)24x21=1
(yk)2b2(xh)2a2=1
h=0,k=1,
a2=1,b2=4
a1,b=2
vertex =(h,k±b)=(0,1±2)=(0,1),(0,3)
Foci =(h,k±a2+b2=(0,1±1+4=(0,1+5),(0,15)
Answer:
vertex =(0,1),(0,3)
Foci =(0,1+5),(0,15)
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