usagirl007A

2021-01-15

To calculate: The equation

timbalemX

Skilled2021-01-16Added 108 answers

Step 1Formula: The general equation of the hyperbola is $\frac{{x}^{2}}{{a}^{2}}\text{}-\text{}\frac{{y}^{2}}{{b}^{2}}=1$ where coordinate of the focus $(\pm \text{}c,\text{}0)\text{}\text{and}\text{}{c}^{2}={a}^{2}\text{}+\text{}{b}^{2}$ Step 2Calculation:Consider the equation of the conic sections$100{y}^{2}\text{}+\text{}4x={x}^{2}\text{}+\text{}104$ That is$100{y}^{2}\text{}-\text{}{x}^{2}\text{}+\text{}4x=104$

$100{y}^{2}\text{}-\text{}({x}^{2}\text{}-\text{}4x)=104$

$100{y}^{2}\text{}-\text{}({x}^{2}\text{}-\text{}4x\text{}+\text{}4)=104\text{}-\text{}4$

$100{y}^{2}\text{}-\text{}{(x\text{}-\text{}2)}^{2}=100$ Or,$\frac{{y}^{2}}{1}\text{}-\text{}\frac{{(x\text{}-\text{}2)}^{2}}{{10}^{2}}=1$ Therfore the standard form of the conic section is$\frac{{y}^{2}}{1}\text{}-\text{}\frac{{(x\text{}-\text{}2)}^{2}}{{10}^{2}}=1$ And since, general equation of the hyperbola is $\frac{{x}^{2}}{{a}^{2}}\text{}-\text{}\frac{{y}^{2}}{{b}^{2}}=1$ , hence, it's a hyperbola.

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