A community for students. Sign up today!
Here's the question you clicked on:
 0 viewing
 2 years ago
What are the foci of the hyperbola given by the equation 16x2  25y2  64x  50y  361 = 0?
 2 years ago
What are the foci of the hyperbola given by the equation 16x2  25y2  64x  50y  361 = 0?

This Question is Closed

helder_edwin
 2 years ago
Best ResponseYou've already chosen the best response.0complete the squares

HopelessMathStudent
 2 years ago
Best ResponseYou've already chosen the best response.0(1 ± , 2) (2 ± , 1) (1, 2 ± ) (2, 1 ± )

HopelessMathStudent
 2 years ago
Best ResponseYou've already chosen the best response.0Its one of these lol Im just not sure which

helder_edwin
 2 years ago
Best ResponseYou've already chosen the best response.0first factor the coeficientes of the squared terms (i rearranged the terms) \[ \large 16x^264x25y^250=361 \] \[ \large 16(x^24x+\qquad)25(y^2+2y+\qquad)=361 \]

HopelessMathStudent
 2 years ago
Best ResponseYou've already chosen the best response.0Kinda but what are the blank spaces?

helder_edwin
 2 years ago
Best ResponseYou've already chosen the best response.0there's a "y" missing next to the 50.

HopelessMathStudent
 2 years ago
Best ResponseYou've already chosen the best response.0Pretty sure its A or B right?

helder_edwin
 2 years ago
Best ResponseYou've already chosen the best response.0now in each parenthesis there's a blank. u have to write there coeficient of the linear term (no power) halved and then squared \[ \large \color{green}{16}(x^24x+\color{red}{4})\color{orange}{25}(y^2+2y+\color{red}{1})=361 +\color{green}{16}\cdot\color{red}{4}\color{orange}{25}\cdot\color{red}{1} \]

helder_edwin
 2 years ago
Best ResponseYou've already chosen the best response.0now \[ \large 16(x\color{red}{2})^225(y\color{red}{+1})^2=400 \] \[ \large \frac{16(x\color{red}{2})^2}{400}\frac{25(y(\color{red}{1}))^2}{400}=1 \] \[ \large \frac{(x\color{red}{2})^2}{25}\frac{(y(\color{red}{1}))^2}{16}=1 \]

helder_edwin
 2 years ago
Best ResponseYou've already chosen the best response.0now the center of the hyperbola is \[ \large (\color{red}{2},\color{red}{1}) \]

helder_edwin
 2 years ago
Best ResponseYou've already chosen the best response.0is it a horizontal or vertical hyperbola? how can u tell?

HopelessMathStudent
 2 years ago
Best ResponseYou've already chosen the best response.0the format of the equation.

helder_edwin
 2 years ago
Best ResponseYou've already chosen the best response.0look at the denominators which is larger? under x? or under y?

helder_edwin
 2 years ago
Best ResponseYou've already chosen the best response.0yes. this tells u the hyperbola is horizontal

HopelessMathStudent
 2 years ago
Best ResponseYou've already chosen the best response.0I said it was horizontal. Is it B?

helder_edwin
 2 years ago
Best ResponseYou've already chosen the best response.0what is the length of the semimayor axis?

helder_edwin
 2 years ago
Best ResponseYou've already chosen the best response.0it HAS to. do u know why?

HopelessMathStudent
 2 years ago
Best ResponseYou've already chosen the best response.0because the formula is formatted (h±a,k) for horizontal and that fits? lol

helder_edwin
 2 years ago
Best ResponseYou've already chosen the best response.0yes. very clever. u were looking for the foci not the vertices, though.

HopelessMathStudent
 2 years ago
Best ResponseYou've already chosen the best response.0do it is B? :) and yeah pretty much lol
Ask your own question
Ask a QuestionFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.