Question 1087977
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Find the center, vertices, foci and asymptotes for the hyperbola 25x^2 - 4y^2 = 100.
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<pre>
{{{25x^2 - 4y^2}}} = 100  ====>  (divide by 100 both sides)  ====>

{{{x^2/4}}} - {{{y^2/25}}} = 1.


The center is (0,0), the origin.

The real axis is horizontal line y = 0, coinciding with x-axis.

The vertices are (-2,0) and (2,0), where 2 - {{{sqrt(4)}}}.

The distance from the center to either focus is c = {{{sqrt(4 + 25)}}} = {{{sqrt(29)}}}.
</pre>

See the lessons

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Quadratic-relations-and-conic-sections/Hyperbola-definition--canonical-equation--characteristic-points-and-elements.lesson>Hyperbola definition, canonical equation, characteristic points and elements</A> 


&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Quadratic-relations-and-conic-sections/Standard-equation-of-a-hyperbola.lesson>Standard equation of a hyperbola</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Quadratic-relations-and-conic-sections/Identify-elements-of-a-hyperbola-given-by-its-standard-eqn-NEW.lesson>Identify elements of hyperbola given by its standard equation</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Quadratic-relations-and-conic-sections/Find-the-standard-equation-of-a-hyperbola-given-by-its-elements.lesson>Find the standard equation of a hyperbola given by its elements</A> 


&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Quadratic-relations-and-conic-sections/REVIEW-of-lessons-on-hyperbolas.lesson>OVERVIEW of lessons on hyperbolas</A> 

in this site.



Also, &nbsp;you have this free of charge online textbook in ALGEBRA-II in this site

&nbsp;&nbsp;&nbsp;&nbsp;<A HREF=https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-II - YOUR ONLINE TEXTBOOK</A>.


The referred lesson is the part of this online textbook under the topic 
"<U>Conic sections: Hyperbolas. Definition, major elements and properties. Solved problems</U>".