Question

Find a polar equation of the hyperbola (x/11)^2−(y/10)^2=1. r^2=?

Answer 1

\(\bf (x/11)^2−(y/10)^2=1. r^2=?\\
\left(\cfrac{x}{11}\right)^2-\left(\cfrac{y}{10}\right)^2=1\implies \cfrac{x^2}{11^2}-\cfrac{y^2}{10^2}=1\qquad {\color{brown}{ \times (11^2\cdot 10^2)}}
\\ \quad \\
{\color{brown}{ (\cancel{ 11^2 }\cdot 10^2)\times }}\cfrac{x^2}{\cancel{ 11^2 }}-{\color{brown}{ (11^2\cdot \cancel{ 10^2 })\times }}\cfrac{y^2}{\cancel{ 10^2 }}={\color{brown}{ (11^2\cdot 10^2)\times }}1
\\ \quad \\
10^2x^2-11^2y^2=(11^2\cdot 10^2)\implies (10x)^2-(11y)^2=12100
\\ \quad \\\
[10rcos(\theta)]^2-[11rsin(\theta)]^2=12100
\\ \quad \\
10^2{\color{olive}{ r^2}}cos^2(\theta)-11^2{\color{olive}{ r^2}}sin(\theta)=12100\)

take common factor, and solve for \(\bf r^2\)