Resourcesdown chevron
Testimonials
Plans
Sign in
Sign up
Resourcesright arrow
Testimonials
Plans
Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

The equation of an ellipse is given below. ((x+13)^(2))/(400)+((y+6)^(2))/(625)=1 What are the foci of this ellipse? Choose 1 answer: (A) (-13+sqrt15,-6) and (-13-sqrt15,-6) (B) (-13,-21) and (-13,9) (c) (-28,-6) and (2,-6) (D) (-13,-6+sqrt15) and (-13,-6-sqrt15)

The equation of an ellipse is given below.\newline(x+13)2400+(y+6)2625=1 \frac{(x+13)^{2}}{400}+\frac{(y+6)^{2}}{625}=1 \newlineWhat are the foci of this ellipse?\newlineChoose 11 answer:\newline(A) (−13+15,−6) (-13+\sqrt{15},-6) and (−13−15,−6) (-13-\sqrt{15},-6) \newline(B) (−13,−21) (-13,-21) and (−13,9) (-13,9) \newline(C) (−28,−6) (-28,-6) and (2,−6) (2,-6) \newline(D) (−13,−6+15) (-13,-6+\sqrt{15}) and (−13,−6−15) (-13,-6-\sqrt{15})

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Algebra 1right chevron icon
Compare linear, exponential, and quadratic growthright chevron icon

Full solution

Q. The equation of an ellipse is given below.\newline(x+13)2400+(y+6)2625=1 \frac{(x+13)^{2}}{400}+\frac{(y+6)^{2}}{625}=1 \newlineWhat are the foci of this ellipse?\newlineChoose 11 answer:\newline(A) (−13+15,−6) (-13+\sqrt{15},-6) and (−13−15,−6) (-13-\sqrt{15},-6) \newline(B) (−13,−21) (-13,-21) and (−13,9) (-13,9) \newline(C) (−28,−6) (-28,-6) and (2,−6) (2,-6) \newline(D) (−13,−6+15) (-13,-6+\sqrt{15}) and (−13,−6−15) (-13,-6-\sqrt{15})
  1. Ellipse Equation: The equation of an ellipse is given by:\newline(x+13)2400+(y+6)2625=1\frac{(x+13)^2}{400} + \frac{(y+6)^2}{625} = 1\newlineTo find the foci of the ellipse, we need to identify the major and minor axes. The denominators of the fractions represent the squares of the semi-major and semi-minor axes lengths. The larger denominator corresponds to the square of the semi-major axis length, and the smaller denominator corresponds to the square of the semi-minor axis length.
  2. Identifying Axes: In the given equation, the denominator 625625 is larger than 400400, which means that the semi-major axis is along the y-axis. The length of the semi-major axis is the square root of 625625, which is 2525. The length of the semi-minor axis is the square root of 400400, which is 2020.
  3. Calculating Semi-Major and Semi-Minor Axes: The foci of an ellipse are located along the major axis at a distance 'c' from the center, where 'c' is found using the equation c=a2−b2c = \sqrt{a^2 - b^2}, where 'a' is the length of the semi-major axis and 'b' is the length of the semi-minor axis.
  4. Finding 'c': We calculate 'c' using the lengths of the semi-major and semi-minor axes:\newlinec=252−202=625−400=225=15c = \sqrt{25^2 - 20^2} = \sqrt{625 - 400} = \sqrt{225} = 15
  5. Determining Center of the Ellipse: The center of the ellipse is at the point (−13,−6)(-13, -6), as indicated by the terms (x+13)(x+13) and (y+6)(y+6) in the equation. Since the major axis is along the y-axis, the foci will be located at (−13,−6±c)(-13, -6 \pm c).
  6. Calculating Foci: Substituting the value of cc into the coordinates of the foci, we get:\newlineFoci: (−13,−6+15)(-13, -6 + 15) and (−13,−6−15)(-13, -6 - 15)\newlineSimplifying the coordinates, we get:\newlineFoci: (−13,9)(-13, 9) and (−13,−21)(-13, -21)

More problems from Compare linear, exponential, and quadratic growth

Question
Jill bought a used motorcycle from a seller online for $1,200. The seller will charge her $5 a day to store the motorcycle at his house until she is able to pick it up. You can use a function to describe the total amount of money Jill will owe the seller if she waits xx days to pick up the motorcycle.\newlineWrite an equation for the function. If it is linear, write it in the form g(x)=mx+bg(x) = mx + b. If it is exponential, write it in the form g(x)=a(b)xg(x) = a(b)^x.\newlineg(x)=‾g(x) = \underline{\hspace{3em}}
Get tutor helpright-arrow

Posted 8 months ago

Question
How does f(t)=−2t−7f(t)=-2t-7 change over the interval from t=−7t=-7 to t=−6t=-6?\newlineChoices:\newline[f(t) decreases by 2]\left[\text{f(t) decreases by } 2\right]\newline[f(t) increases by 2]\left[\text{f(t) increases by } 2\right]\newline[f(t) increases by 200%]\left[\text{f(t) increases by } 200\%\right]\newline[f(t) decreases by a factor of 2]\left[\text{f(t) decreases by a factor of } 2\right]
Get tutor helpright-arrow

Posted 8 months ago

Question
How does g(t)=9tg(t)=9^t change over the interval from t=1t=1 to t=3t=3?\newlineChoices: \newline[g(t) decreases by a factor of 81]\left[\text{g(t) decreases by a factor of } 81\right]\newline[g(t) increases by a factor of 81]\left[\text{g(t) increases by a factor of } 81\right]\newline[g(t) increases by 18%]\left[\text{g(t) increases by } 18\%\right]\newline[g(t) decreases by 9%]\left[\text{g(t) decreases by } 9\%\right]
Get tutor helpright-arrow

Posted 8 months ago

Question
Both of these functions grow as xx gets larger and larger. Which function eventually exceeds the other?\newline Choices:\newline(A)f(x)=8x+3.3(A)f(x) = 8x + 3.3\newline(B)g(x)=3.3x−5(B)g(x) = 3.3^x - 5
Get tutor helpright-arrow

Posted 9 months ago

Question
Both of these functions grow as x x gets larger and larger. Which function eventually exceeds the other?\newlineChoices:\newline(A) f(x)=2x+9(A) \ f(x) = 2x + 9 \newline(B) g(x)=2x(B)\ g(x) = 2^x
Get tutor helpright-arrow

Posted 9 months ago

Question
The functions f(x) f(x) and g(x) g(x) are differentiable. \newlineThe function h(x) h(x) is defined as: h(x)=g(x)f(x) h(x)=\frac{g(x)}{f(x)} \newlineIf f(8)=1 f(8)=1 , f′(8)=−6 f'(8)=-6 , g(8)=8 g(8)=8 , and g′(8)=−10 g'(8)=-10 , what is h′(8) h'(8) ? \newlineSimplify any fractions. \newlineh′(8)= h'(8)= ______
Get tutor helpright-arrow

Posted 8 months ago

Question
The functions p(x) p(x) and q(x) q(x) are differentiable. \newlineThe function r(x) r(x) is defined as: r(x)=p(x)q(x) r(x)= \frac{p(x)}{q(x)} \newlineIf p(3)=2 p(3)= 2 , p′(3)=4 p'(3)= 4 , q(3)=6 q(3)= 6 , and q′(3)=9 q'(3)= 9 , what is r′(3) r'(3) ? \newlineSimplify any fractions. \newliner′(3)= r'(3)= _____
Get tutor helpright-arrow

Posted 9 months ago

Question
The functions u(x) u(x) and v(x) v(x) are differentiable. \newlineThe function w(x) w(x) is defined as: w(x)=u(x)v(x) w(x)= \frac{u(x)}{v(x)} \newlineIf u(5)=3 u(5)= 3 , u′(5)=−2 u'(5)= -2 , v(5)=7 v(5)= 7 , and v′(5)=1 v'(5)= 1 , what is w′(5) w'(5) ? \newlineSimplify any fractions. \newlinew′(5)= w'(5)= _____
Get tutor helpright-arrow

Posted 9 months ago

Question
The functions a(x) a(x) and b(x) b(x) are differentiable. \newlineThe function c(x) c(x) is defined as: c(x)=a(x)b(x) c(x)= \frac{a(x)}{b(x)} \newlineIf a(2)=4 a(2)= 4 , a′(2)=5 a'(2)= 5 , b(2)=1 b(2)= 1 , and b′(2)=−3 b'(2)= -3 , what is c′(2) c'(2) ? \newlineSimplify any fractions. \newlinec′(2)= c'(2)= _____
Get tutor helpright-arrow

Posted 9 months ago

Question
The functions m(x) m(x) and n(x) n(x) are differentiable. \newlineThe function o(x) o(x) is defined as: o(x)=m(x)n(x) o(x)= \frac{m(x)}{n(x)} \newlineIf m(7)=2 m(7)= 2 , m′(7)=−1 m'(7)= -1 , n(7)=4 n(7)= 4 , and n′(7)=8 n'(7)= 8 , what is o′(7) o'(7) ? \newlineSimplify any fractions. \newlineo′(7)= o'(7)= _____
Get tutor helpright-arrow

Posted 9 months ago

View all (100)

Related topics

Algebra - Order of OperationsAlgebra - Distributive Property`X` and `Y` AxesGeometry - Scalene TriangleCommon MultipleGeometry - Quadrant