Question

# Sketch the following conic sections: 4^{2}-4y+8-4x^{2}=0

Conic sections
Sketch the following conic sections:
$$\displaystyle{4}^{{{2}}}-{4}{y}+{8}-{4}{x}^{{{2}}}={0}$$

2021-08-16
Step 1
Given Equation: $$\displaystyle{y}^{{{2}}}-{4}{y}+{8}-{4}{x}^{{{2}}}={0}$$
Converting the above equation in Standard hyperbola form standard form
$$\displaystyle{\frac{{{\left({x}-{h}\right)}^{{{2}}}}}{{{a}^{{{2}}}}}}-{\frac{{{\left({y}-{k}\right)}^{{{2}}}}}{{{b}^{{{2}}}}}}={1}$$
The above equation in Standard form
$$\displaystyle{x}^{{{2}}}-{\frac{{{\left({y}-{2}\right)}^{{{2}}}}}{{{4}}}}={1}$$
comparing with the standard form we have $$\displaystyle{h}={0},\ {a}={1},\ {k}={2},\ {b}={2}$$
Step 2
The graph of the above equation is shown below