**High School Number Sense Lesson 94: Ellipses**

Today's concept appeared

**8 times**this year, with a median placement at

**question # 57**.

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There are several formulas that need to be learned to find the properties of ellipses. In each case, the equation for the ellipse will be presented with the format:

**Ax**

^{2}+ By^{2}= C**Formulas:**

- Area = π√(AB)
- Length of Major Axis = the larger of 2√A or 2√B
- Length of Minor Axis = the smaller of 2√A or 2√B

**Example 1:**

**The area of the ellipse 9x**

^{2}+ 4y^{2}= 36 is kπ. Find k. ___1. Area = π√(AB)

2. √(AB) = √(9 x 4) = √36 =

**6**

**Example 2:**

**The length of the minor axis of 9x**

^{2}+ 4y^{2}= 36 is ___1. Find √A and √B.

2. √A = √9 =

**3**. √B = √4 =

**2**.

3. The length of the minor axis is twice the smaller of these, so 2 x 2 =

**4**

**Example 3:**

**The length of the major axis of 5x**

^{2}+ 9y^{2}= 45 is ___1. √5 < √9 (which is 3).

2. The length of the major axis is twice the larger of these, so 2 x 3 =

**6**

**Example 4:**

**The sum of the lengths of the minor axis and the major axis of 4x**

^{2}+ 9y^{2}= 36 is ___1. √4 = 2; √9 = 3

2. The length of the axes is twice these results, so

**4 and 6**

3. 4 + 6 =

**10**

**Example 5:**

**The length of the minor axis of 8x**

^{2}+ 12y^{2}= 96 is p√q. Find p + q.1. √8 = 2√2. √12 = 3√2.

2. The length of the minor axis is twice the smaller of these, so 2 x 2√2 =

**4√2**

3. p = 4 and q = 2. 4 + 2 =

**6**

**Up Next for High School: TrigSinCos**