The center of an ellipse is located at (0, 0). One focus is located at (12, 0), and one directrix is at x = 14 1/12.
2 answers:
The standard equation for an ellipse is
where
(h,k) = coordinates of the center
a, b = semi-major and semi-minor axes
Refer to the figure shown below.
The center of the ellipse is at (0,0).
Therefore, h=0, k=0.
One focus is at (12, 0)
Therefore
c = 12
One directrix is at 14 1/12 = 169/12.
Because the directrix is located at x = a²/c, therefore
a²/12 = 169/12
a² = 169/144
a = 13
Because c² = a² - b², obtain
b² = a² - c²
= 169 - 144 = 25
b = 5
Answer:
The equation for the ellipse is
where
(h,k) = coordinates of the center
a, b = semi-major and semi-minor axes
Refer to the figure shown below.
The center of the ellipse is at (0,0).
Therefore, h=0, k=0.
One focus is at (12, 0)
Therefore
c = 12
One directrix is at 14 1/12 = 169/12.
Because the directrix is located at x = a²/c, therefore
a²/12 = 169/12
a² = 169/144
a = 13
Because c² = a² - b², obtain
b² = a² - c²
= 169 - 144 = 25
b = 5
Answer:
The equation for the ellipse is
You might be interested in
Answer:
The equation of the hypotenuse line is y = -3·x + 9
Therefore, the correct options are -3 and 9
Step-by-step explanation:
The question asks to fill the boxes
y = _ x + _
We note that the equation is that of a straight line of the form;
y = m·x + c
Where:
m = Slope of the straight line graph and
c = Y intercept, that is the y-coordinate of the point on the line where x = 0
From the graph, we find the slope as follows;
Therefore, m = -3
The y intercept is found by extending the hypotenuse line to the point where it touches the y axes that is at x = 0;
From the graph, it is observed that the line, when extended, touches the y axes at the point y = 9, therefore, c = 9
Hence we have, the equation of the hypotenuse line is y = -3·x + 9.