Posts Tagged ‘vertices’

Problem 1075

Determine whether the following statement is true or false.

A tree is a complete graph.

 

Solution:-

 

The statement is false. A tree does not have an edge between each pair of its vertices.

 

 

 

Problem 522

What are the co-vertices of the following graph?

522

 

Solution: –

 

This is an ellipse with a center at (-1, 0), foci (-1 – \sqrt{3} , 0) and (-1 + \sqrt{3}  , 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?

521

 

Solution:-

 

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

 

So the  equation is \frac{(x+1)^2}{4}+\frac{y^2}{1} = 1

 

 

Problem 520

What are the vertices of the following graph?

520

 

Solution:-

 

This is an ellipse with a center at (-1, 0), foci (-1 – \frac{3} , 0) and (-1 + \frac{3}  , 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?

519

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 517

 

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

517

 

Solution:-

 

This is an ellipse with a center at (0, 0), vertices at (0, -6) and (0, 6), co-vertices at (-3, 0) and (3, 0), the major axis has a length of 12 and the minor axis has a length of 6, the foci are (0,-\sqrt{27}) and (0, \sqrt{27}).

 

So the  length of the major axis is 12.