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Problem 1143

Find the eccentricity of the ellipse

Solution:-

eccentricity of the ellipse = c/a

c = √(a^2 – b^2)

c = √(25-5)

c= √(20)

c = 2√(5)

eccentricity = (2√5)/5

Problem 718

Find the eccentricity of the ellipse

Solution:-

eccentricity of the ellipse =

c =

c =

c=

c =

eccentricity =

Problem 522

What are the co-vertices of the following graph?

Solution: –

This is an ellipse with a center at (-1, 0), foci (-1 –  , 0) and (-1 +   , 0), vertices (-3, 0) and (1, 0) and co-vertices (-1, -1) and (-1, 1).

So the co-vertices is (-1, -1) and (-1, 1).

Problem 521

What is the equation of the following graph?

Solution:-

This is an ellipse with a center at (-1, 0), foci (-1 –    , 0) and (-1 +   , 0), vertices (-3, 0) and (1, 0) and co-vertices (-1, -1) and (-1, 1).

So the  equation is

Problem 520

What are the vertices of the following graph?

Solution:-

This is an ellipse with a center at (-1, 0), foci (-1 –  , 0) and (-1 +   , 0), vertices (-3, 0) and (1, 0) and co-vertices (-1, -1) and (-1, 1).

So the vertices is (-3, 0) and (1, 0).

Problem 519

What are the vertices of the following graph?

Solution:-

This is an ellipse with a center at (0, 0), vertices at (-5, 0) and (5, 0), co-vertices at (0, 3) and (0, -3), the major axis has a length of 10 and the minor axis has a length of 6, the foci are (-4, 0) and (4, 0).

So the vertices is (-5, 0) and (5, 0).

Problem 518

What is the length of the minor axis of the following graph?

Solution:-

This is an ellipse with a center at (0, 0), vertices at (-5, 0) and (5, 0), co-vertices at (0, 3) and (0, -3), the major axis has a length of 10 and the minor axis has a length of 6, the foci are (-4, 0) and (4, 0).

So the minor axis is 6.