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 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?

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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
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