What are the foci of the hyperbola represented by the equation (y^(2))/(41)-(x^(2))/(25)=1? Choose 1 answer: (A) (4,0) and (-4,0) (B) (sqrt66,0) and (-sqrt66,0) (c) (0,sqrt66) and (0,-sqrt66) (D) (0,4) and (0,-4)

Hyperbola Equation Form: The given equation is in the form of a hyperbola with the equation $\frac{y^2}{a^2} - \frac{x^2}{b^2} = 1$, where $a^2$ is under the $y^2$ term and $b^2$ is under the $x^2$ term. This indicates that the hyperbola opens up and down along the y-axis.Finding the Foci: To find the foci of the hyperbola, we need to use the formula $c^2 = a^2 + b^2$, where $c$ is the distance from the center to each focus.Calculating c^2: From the given equation, we can see that $a^2 = 41$ and $b^2 = 25$. Now we will calculate $c^2$.Substituting Values: Substitute the values of $a^2$ and $b^2$ into the formula to find $c^2$: $c^2 = 41 + 25$.Calculating c: Calculate $c^2$: $c^2 = 66$.Locating the Foci: Now, find the value of $c$ by taking the square root of $c^2$: $c = \sqrt{66}$.Finding the Coordinates: Since the hyperbola opens up and down, the foci are located at $(0, \pm c)$ along the y-axis.Substitute the value of $c$ to find the coordinates of the foci: $(0, \sqrt{66})$ and $(0, -\sqrt{66})$.

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What are the foci of the hyperbola represented by the equation
(y^(2))/(41)-(x^(2))/(25)=1?
Choose 1 answer:
(A)
(4,0) and
(-4,0)
(B)
(sqrt66,0) and
(-sqrt66,0)
(c)
(0,sqrt66) and
(0,-sqrt66)
(D)
(0,4) and
(0,-4)

What are the foci of the hyperbola represented by the equation $\frac{y^{2}}{41}-\frac{x^{2}}{25}=1 ?$ $\newline$ Choose $1$ answer: $\newline$ (A) $(4,0)$ and $(-4,0)$ $\newline$ (B) $(\sqrt{66}, 0)$ and $(-\sqrt{66}, 0)$ $\newline$ (C) $(0, \sqrt{66})$ and $(0,-\sqrt{66})$ $\newline$ (D) $(0,4)$ and $(0,-4)$

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Q. What are the foci of the hyperbola represented by the equation

\frac{y^{2}}{41}-\frac{x^{2}}{25}=1 ?

\newline

Choose

1

answer:

\newline

(A)

(4,0)

and

(-4,0)

\newline

(B)

(\sqrt{66}, 0)

and

(-\sqrt{66}, 0)

\newline

(C)

(0, \sqrt{66})

and

(0,-\sqrt{66})

\newline

(D)

(0,4)

and

(0,-4)

Hyperbola Equation Form: The given equation is in the form of a hyperbola with the equation $\frac{y^2}{a^2} - \frac{x^2}{b^2} = 1$ , where $a^2$ is under the $y^2$ term and $b^2$ is under the $x^2$ term. This indicates that the hyperbola opens up and down along the y-axis.
Finding the Foci: To find the foci of the hyperbola, we need to use the formula $c^2 = a^2 + b^2$ , where $c$ is the distance from the center to each focus.
Calculating c^ $2$ : From the given equation, we can see that $a^2 = 41$ and $b^2 = 25$ . Now we will calculate $c^2$ .
Substituting Values: Substitute the values of $a^2$ and $b^2$ into the formula to find $c^2$ : $c^2 = 41 + 25$ .
Calculating c: Calculate $c^2$ : $c^2 = 66$ .
Locating the Foci: Now, find the value of $c$ by taking the square root of $c^2$ : $c = \sqrt{66}$ .
Finding the Coordinates: Since the hyperbola opens up and down, the foci are located at $(0, \pm c)$ along the y-axis.
Finding the Coordinates: Since the hyperbola opens up and down, the foci are located at $(0, \pm c)$ along the y-axis.Substitute the value of $c$ to find the coordinates of the foci: $(0, \sqrt{66})$ and $(0, -\sqrt{66})$ .