Find Equation of Elipse with b=3, M(-2SQRT(5),2)

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In summary, an ellipse is a flattened circle with a curved perimeter and two focal points. To find the equation of an ellipse with a given center and length of the semi-minor axis, the standard form of the ellipse equation can be used. The significance of b in the equation represents the length of the semi-minor axis and helps determine the shape and size of the ellipse. To graph an ellipse, the center point and the lengths of the semi-major and semi-minor axes are needed to plot points on the major and minor axes and sketch the ellipse. The main difference between an ellipse and a circle is the varying distances from the center to points on their perimeters and the number of radii (one for a circle, two for an
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Government$
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Homework Statement


Find equation of elips if b=3 and point M(-2SQRT(5), 2) is on elipse.

Homework Equations



x^2/a^2 + y^2/b^2 = 1

The Attempt at a Solution


x^2/a^2 + y^2/b^2 = 1

20/a^2 + 4/9 = 1

20/a^2 + 4/9 = 1 / * a^2

20 + 4a^2/9 = a^2

20 + 4^2 = 9a^2

20= 5a^2

a = 2

so equation of elipse is x^2/4 + y^2/9 = 1

But answer at the end of a book is 9x^2 + 36y^2 = 324

Which one is correct?
 
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This bit:

20 + 4a^2/9 = a^2

20 + 4a^2 = 9a^2

is wrong, because you should multiply the 20 by 9 too. Equation should become

180 + 4a^2 = 9a^2, which would give you the right solution.
 

FAQ: Find Equation of Elipse with b=3, M(-2SQRT(5),2)

What is an ellipse?

An ellipse is a type of geometric shape that resembles a flattened circle. It has a curved perimeter and two focal points, which are equidistant from the center of the ellipse.

How do you find the equation of an ellipse with b=3 and center at M(-2√5,2)?

The equation of an ellipse with b=3 and center at M(-2√5,2) can be found using the standard form of the ellipse equation:
(x-h)^2/a^2 + (y-k)^2/b^2 = 1
where (h,k) is the center of the ellipse and a and b are the lengths of the semi-major and semi-minor axes. Plugging in the given values, we get the equation:
(x+2√5)^2/9 + (y-2)^2/3 = 1

What is the significance of b in the equation of an ellipse?

b represents the length of the semi-minor axis of the ellipse. It is half the length of the minor axis, which is the shorter diameter of the ellipse. It helps determine the shape and size of the ellipse.

How do you graph an ellipse with the given equation?

To graph an ellipse with the equation (x+2√5)^2/9 + (y-2)^2/3 = 1, first find the center point at (-2√5,2). Then, plot the two points on the major axis by adding and subtracting the length of the semi-major axis (3) from the x-coordinate of the center point. Next, plot the two points on the minor axis by adding and subtracting the length of the semi-minor axis (2) from the y-coordinate of the center point. Finally, sketch the ellipse through these points.

What is the difference between an ellipse and a circle?

An ellipse and a circle are different types of geometric shapes. A circle has a constant distance from the center to any point on its perimeter, while an ellipse has varying distances from the center to points on its perimeter. Additionally, a circle has a single radius, while an ellipse has two radii – one for the semi-major axis and one for the semi-minor axis.

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