Write the equation of the ellipse that satisfies the given conditions. Sketch th...

Questions

August 2022 1 2 Report

Write the equation of the ellipse that satisfies the given conditions. Sketch the graph.

1. Center at (6, 1), vertex (6, -4), end of minor axis at (3,1)

2. Vertex at (5,2), foci at (-4,2) and (4,2)

3. Ends of minor axis at ( -2,2) and (-2, -4), focus at (2, -1)

4. Vertices at (-2,3) and (8,3), length of minor axis 8.

5. Center at (2,3), one vertex at (2,8), end of minor axis at (6,3)

Answers & Comments

KallesElias

Write the equation of the ellipse that satisfies the given conditions. Sketch the graph.

Problem 1:

1. Center at (6, 1), vertex (6, -4), end of minor axis at (3,1)

Solution:

plot every given coordinates on the graph so that it will be easy to identify the values of a and b

Center (h, k)

Center at (6, 1)

from the graph,

a = 3

b = 5

$\begin{array}{l}\frac{{{{(x - h)}^2}}}{{{a^2}}} + \frac{{{{(y - k)}^2}}}{{{b^2}}} = 1\\\\\frac{{{{(x - 6)}^2}}}{{{3^2}}} + \frac{{{{(y - 1)}^2}}}{{{5^2}}} = 1\\\\\frac{{{{(x - 6)}^2}}}{9} + \frac{{{{(y - 1)}^2}}}{{{{25}}}} = 1\end{array}$ → equation of the ellipse

Problem 2:

2. Vertex at (5,2), foci at (-4,2) and (4,2)

Solution:

plot every given coordinates on the graph so that it will be easy to identify the values of a and c. then calculate for b

from the graph,

a = 5

c = 4

c² = a² - b²

-b² = c² - a²

b² = a² - c²

b² = 5² - 4²

b² = 25 - 16

b² = 9

Center(0, 2)

$\begin{array}{l}\frac{{{{(x - k)}^2}}}{{{a^2}}} + \frac{{{{(y - k)}^2}}}{{{b^2}}} = 1\\\\\frac{{{{(x - 0)}^2}}}{{{5^2}}} + \frac{{{{(y - 2)}^2}}}{{{3^2}}} = 1\\\\\frac{{{{(x)}^2}}}{{25}} + \frac{{{{(y - 2)}^2}}}{9} = 1\end{array}$ → equation of the ellipse

Problem 3:

3. Ends of minor axis at ( -2,2) and (-2, -4), focus at (2, -1)

plot every given coordinates on the graph so that it will be easy to identify the values of a and c. then calculate for b

from the graph,

a = 5

c = 4

c² = a² - b²

-b² = c² - a²

b² = a² - c²

b² = 5² - 4²

b² = 25 - 16

b² = 9

Center(-2, -1)

$\begin{array}{l}\frac{{{{(x - k)}^2}}}{{{a^2}}} + \frac{{{{(y - k)}^2}}}{{{b^2}}} = 1\\\\\frac{{{{(x + 2)}^2}}}{{{5^2}}} + \frac{{{{(y + 1)}^2}}}{{{3^2}}} = 1\\\\\frac{{{{(x + 2)}^2}}}{{25}} + \frac{{{{(y + 1)}^2}}}{9} = 1\end{array}$ → equation of the ellipse

Problem 4:

4. Vertices at (-2,3) and (8,3), length of minor axis 8.

plot every given coordinates on the graph so that it will be easy to identify the values of a and b

Center (h, k)

Center at (3, 3)

from the graph,

a = 5

b = 4

$\begin{array}{l}\frac{{{{(x - k)}^2}}}{{{a^2}}} + \frac{{{{(y - k)}^2}}}{{{b^2}}} = 1\\\\\frac{{{{(x - 3)}^2}}}{{{5^2}}} + \frac{{{{(y - 3)}^2}}}{{{4^2}}} = 1\\\\\frac{{{{(x - 3)}^2}}}{{25}} + \frac{{{{(y - 3)}^2}}}{{16}} = 1\end{array}$ → equation of the ellipse

Problem 5:

5. Center at (2,3), one vertex at (2,8), end of minor axis at (6,3)

plot every given coordinates on the graph so that it will be easy to identify the values of a and b

Center (h, k)

Center at (2, 3)

from the graph,

a = 4

b = 5

$\frac{{{{(x - k)}^2}}}{{{a^2}}} + \frac{{{{(y - k)}^2}}}{{{b^2}}} = 1$

$\frac{{{{(x - 2)}^2}}}{{{4^2}}} + \frac{{{{(y - 3)}^2}}}{{{5^2}}} = 1$

$\frac{{{{(x - 2)}^2}}}{{16}} + \frac{{{{(y - 3)}^2}}}{{25}} = 1$ → equation of the ellipse

#CarryOnLearning

pengesagotplease25 thankyou po sobra

pengesagotplease25 pwede ko po kayo maging tutor?

pengesagotplease25 hm po?

pengesagotplease25 Ang galing niyo po kasi eh

pengesagotplease25 Wala po akong matutunan kasi eh nahihirapan ako :((

KallesElias baka po pala malito u kasi po ang "a" ko po ay laging nasa x axis at ang "b" ay laging nasa y axis ke mapa vertical man o horizontal ang major axis.

pengesagotplease25 thank u po