Chapter 12: Q. 7 (page 840)

Find the equation of an ellipse with center at the origin, a focus at $(0, 3)$ , and a vertex at $(0, 4)$ .

Short Answer

Expert verified

The equation of ellipse is $\frac{x^{2}}{7} + \frac{y^{2}}{16} = 1$

Step by step solution

Step 1. Given Information

Focus of the ellipse $(0, 3)$ and vertex $(0, 4)$

Focus $= (0, c) = (0, 3)$ and vertex $(0, a) = (0, 4)$ . So $c = 3, a = 4$

Step 2. Finding the value of a,b

By the relation

$c^{2} = a^{2} - b^{2} 3^{2} = 4^{2} - b^{2} b^{2} = 16 - 9 = 7$

Step 3. Equation of Ellipse

$\frac{x^{2}}{b^{2}} + \frac{y^{2}}{a^{2}} = 1 \frac{x^{2}}{7} + \frac{y^{2}}{16} = 1$

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Find the equation of an ellipse with center at the origin, a focus at $(0, 3)$ , and a vertex at $(0, 4)$ .

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Finding the value of a,b

Step 3. Equation of Ellipse

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Find the equation of an ellipse with center at the origin, a focus at 0,3, and a vertex at 0,4.

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Finding the value of a,b

Step 3. Equation of Ellipse

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Probability and Statistics

Statistics

Discrete Mathematics

Pure Maths

Logic and Functions

Study anywhere. Anytime. Across all devices.

Find the equation of an ellipse with center at the origin, a focus at $(0, 3)$ , and a vertex at $(0, 4)$ .