Question

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

Answer 1

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