Identify the conic section given by y2+2y=4x2+3 Find its vertexvertices and focusfoci

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Identify the conic section given by y2+2y=4x2+3  Find its vertexvertices and focusfoci

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Step 1  We rewrite the equation as:  y2+2y=4x2+3  y2+2y−4x2=3  y2+2y+1−4x2=3+1  (y+1)2−4x2=4  (y+1)24−4x24=1  (y+1)24−x21=1  This is an equation of a hyperbola.  Step 2  Then we compare the equation with standard form.  (y+1)24−x21=1  (y−k)2b2−(x−h)2a2=1  h=0,k=−1,  a2=1,b2=4  a−1,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,−1−5)  Answer:  vertex =(0,1),(0,3)  Foci =(0,−1+5),(0,−1−5)

Identify the conic section given by y2+2y=4x2+3 Find its vertexvertices and focusfoci

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