Q 52. Find the centre, foci, and verti... [FREE SOLUTION]

91影视

Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 10: Q 52. (page 655)

Find the centre, foci, and vertices of each ellipse. Graph each equation by hand. Verify your graph using a graphing utility

Short Answer

Expert verified

Vertices of an ellipse. $V_{1} = (0, 1)$ and $V_{2} = (- 6, 1)$

Height of an ellipse at the centre. $B_{1} = (- 3, 0)$ and $B_{2} = (- 3, 2)$

Foci of an ellipse $F_{1} = (- 3 + 2 \sqrt{2,} 1)$ and role="math" localid="1646917784195" $F_{2} = (- 3 - 2 \sqrt{2}, 1)$

Centre of an ellipse. $(- 3, 1)$

Step by step solution

Step 1. Given information.

In order to obtain to get the equation of an ellipse.

$x^{2} + 9 y^{2} + 6 x - 18 y + 9 = 0 (x^{2} + 6 x) + 9 (y^{2} - 2 y) + 9 = 0 (x^{2} + 6 x + 9) + 9 (y^{2} - 2 y + 1) = 0 {(x + 3)}^{2} + 9 {(y - 1)}^{2} = 9 (x + 3)$ ²9+(y-1)2=1

Step 2. The major axis, centre, vertices, foci, the points left and right of the centre.

$\frac{{(x - h)}^{2}}{a^{2}} + \frac{{(y - k)}^{2}}{b^{2}} = 1$ We have seen that the greater denominator, $9$ is located under the x-variable. therefore the ellipse has its major axis parallel to the x-axis.

The equation of an ellipse with its major axis parallel to the y-axis and its centre in $(h, k)$ is $\frac{{(x - h)}^{2}}{a^{2}} + \frac{{(y - k)}^{2}}{b^{2}} = 1$