Write the standard equation of the ellipse with the given characteristics
vertices:(-8,1)(0,1) (-4,7) (-4,5)
center:(-4,1)
I think you have a typo
the centre (-4,1) must be the midpoint for both axes
it works for (-8,1 and (0,1) with 2a = 8 ----> a = 4
but (-4,1) is NOT the midpoint of (-4,7 and (-4,5)
the y values are incorrect
once you have them corrected,
2b = the difference in the y values, b = half of that
then after you have found b, replace it in
(x+4)^2 /4 + (y-1)^2 /b^2 = 1
i'M NOT SURE HOW TO FIND b CAN YOU SHOW ME PLEASE!
Ajay,
Did you not read what I said about the typo?
The way it is you cannot do the question.
Find the error and I can continue helping you.
To write the standard equation of an ellipse, we need the information about its center, vertices, and co-vertices.
The center of the ellipse is given as (-4, 1).
First, let's find the distance between the center and one of the vertices. We can choose either (0, 1) or (-8, 1) since they have the same y-coordinate. Let's choose (0, 1).
The distance between the center and the vertex on the major axis is the length of the major radius (a). In this case, the distance is 4 (the x-coordinate changes from -4 to 0).
Next, let's find the distance between the center and one of the co-vertices. We can choose either (-4, 7) or (-4, 5) since they have the same x-coordinate. Let's choose (-4, 7).
The distance between the center and the co-vertex on the minor axis is the length of the minor radius (b). In this case, the distance is 6 (the y-coordinate changes from 1 to 7).
Now we have all the necessary information to write the standard equation of the ellipse. The equation is:
(x - h)^2/a^2 + (y - k)^2/b^2 = 1
Where (h, k) represents the center of the ellipse, a is the length of the major radius, and b is the length of the minor radius.
Plugging in the values we found:
(x - (-4))^2/4^2 + (y - 1)^2/6^2 = 1
Simplifying the equation:
(x + 4)^2/16 + (y - 1)^2/36 = 1
Therefore, the standard equation of the ellipse with the given characteristics is (x + 4)^2/16 + (y - 1)^2/36 = 1.