Chapter 11: Q. 173E (page 1134)

In the following exercises, a). Write the equation in standard form and b). graph.
$9 y^{2} - x^{2} + 18 y - 4 x - 4 = 0$

Short Answer

Expert verified

Part (a) The equation of hyperbola is $\frac{{(y + 1)}^{2}}{1} - \frac{{(x + 2)}^{2}}{9} = 1$

Part (b) The graph is

Step by step solution

Part (a) Step 1. Given information

The equation is $9 y^{2} - x^{2} + 18 y - 4 x - 4 = 0$ .

Write the equation in standard form of hyperbola and draw the graph.

Part (a) Step 2. Write the equation in standard form of hyperbola

Simplify the equation.

$9 y^{2} - x^{2} + 18 y - 4 x - 4 = 0 9 (y^{2} + 2 y) - (x^{2} + 4 x) = 4$

Covert the equation in complete square

$9 (y^{2} + 2 y + 1) - (x^{2} + 4 x + 4) = 4 + 9 - 4 9 {(y + 1)}^{2} - {(x + 2)}^{2} = 9$

Divide the equation by 9 to get standard form of hyperbola

$\frac{9 {(y + 1)}^{2}}{9} - \frac{{(x + 2)}^{2}}{9} = \frac{9}{9} \frac{{(y + 1)}^{2}}{1} - \frac{{(x + 2)}^{2}}{9} = 1$

Part (b) Step 1. Find centre and asymptote.

In the equation is $\frac{{(y + 1)}^{2}}{1} - \frac{{(x + 2)}^{2}}{9} = 1$

They² term is positive, the transverse axis is vertical.

The hyperbola opens up and down.

Find the centre

Compare the equation with standard form $\frac{{(y - k)}^{2}}{a^{2}} - \frac{{(x - h)}^{2}}{b^{2}} = 1$

So, $(h, k) = (- 2, - 1)$ and $a^{2} = 1 \Rightarrow a = \pm 1$ also $b^{2} = 9 \Rightarrow b = \pm 3$

The rectangle that goes through the points 1 units above/below the centre. 3 units left/right of centre.

Part (b) Step 2. Draw the graph.

Sketch the asymptotes and draw the graph.

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In the following exercises, a). Write the equation in standard form and b). graph.
$9 y^{2} - x^{2} + 18 y - 4 x - 4 = 0$

Short Answer

Step by step solution

Part (a) Step 1. Given information

Part (a) Step 2. Write the equation in standard form of hyperbola

Part (b) Step 1. Find centre and asymptote.

Part (b) Step 2. Draw the graph.

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In the following exercises, a). Write the equation in standard form and b). graph. 9y2-x2+18y-4x-4=0

Short Answer

Step by step solution

Part (a) Step 1. Given information

Part (a) Step 2. Write the equation in standard form of hyperbola

Part (b) Step 1. Find centre and asymptote.

Part (b) Step 2. Draw the graph.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

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Study anywhere. Anytime. Across all devices.

In the following exercises, a). Write the equation in standard form and b). graph.
$9 y^{2} - x^{2} + 18 y - 4 x - 4 = 0$