Posts Tagged ‘ellipse’

Problem 1143

Find the eccentricity of the ellipse   \frac{x^{2}}{25}+\frac{(y-7)^{2}}{5}=1

 

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   \frac{x^{2}}{25}+\frac{(y-7)^{2}}{5}=1

 

Solution:-

 

eccentricity of the ellipse = \frac{c}{a}

c =   \sqrt{a^{2}-b^{2}}

c =  \sqrt{25-5}

c= \sqrt{20}

c =   2\sqrt{5}

eccentricity = \frac{2\sqrt{5}}{5}

 

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 518

 

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

518

 

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.