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In this lesson, we will learn how to find hyperbolas' vertices, foci, and asymptotes from their graphs.

Q1:

The graph shows a sketch of the hyperbola given by the equation 4 π¦ β π₯ + 8 π¦ β 1 0 π₯ = 2 5 2 2 .

Give the coordinates of the center πΆ .

Give the coordinates of the vertices π 1 and π 2 .

Give the coordinates of the foci πΉ 1 and πΉ 2 .

Give the equations of the asymptotes π΄ 1 and π΄ 2 .

Q2:

The graph shows a sketch of the hyperbola given by the equation ( π¦ β 2 ) 2 5 β ( π₯ + 3 ) 2 = 1 2 2 .

Q3:

The graph shows a sketch of the hyperbola given by the equation ( π₯ β 3 ) 4 β ( π¦ β 1 ) 1 6 = 1 ο¨ ο¨ .

Give the coordinates of the vertices π ο§ and π ο¨ .

Give the coordinates of the foci πΉ ο§ and πΉ ο¨ .

Give the equations of the asymptotes π΄ ο§ and π΄ ο¨ .

Q4:

The graph shows a sketch of the hyperbola given by the equation 4 π₯ β 9 π¦ β 1 6 π₯ β 1 8 2 π¦ = 2 9 2 2 .

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