Question

Animation: Investigating the effect of h k a and b on the graph of an ellipse Go past the animation and review examples 1, 2 and 3. 1) Use the animation mentioned earlier on page 910 to create two graphs of two ellipses using the instructions below. (3 pts each). a. Create an ellipse so that the major axis is horizontal and the center is not the origin. State the center and vertices (as points) along with the distance to the minor axis (a numeric value). Include a picture of this ellipse from the animation. b. Create a second ellipse so that the major axis is vertical and the center is not the origin. State the center and vertices (as points) along with the distance to the minor axis (a numeric value). Include a picture of this ellipse from the animation.

Answer 1

A

Given equation is of ellipse is

(x²/a²⁾+(y²/b²)=1

a and b is the focis length

If an ellipse is translated h units horizontally and k units vertically, the center of the ellipse will be (h,k). This translation results in the standard form of the equation we saw previously, with  x replaced (x−h) and y replaced by (y−k).

((x-h)²/a²⁾+((y-k)²/b²)=1

A. The standard form of the equation of an ellipse with center (h, k) and major axis is Horizontal (parallel to the x-axis) is

((x-h)²/a²⁾+((y-k)²/b²)=1

where some properties of ellipse

• In this case a always greater than b i.e a>b
• an ellipse the coordinates of the vertices are (h±a,k)
• an elllipse the coordinates of the co-vertices are (h,k±b)
• the length of the major axis is 2a
• the length of the minor axis is 2b
• In the ellipse the coordinates of the foci are (h±c,k), where c​²​​=a​²−b​²​.

(6,446) minst anys - Shtok) x Shagl.k) (black) fot major amis (h, k/b] origin

B.

The standard form of the equation of an ellipse with center (h, k) and major axis is vertical (parallel to the y-axis) is

((x-h)²/b²⁾+((y-k)²/a²)=1

where some properties

• In this case a always greater than b i.e a>b
• an ellipse the coordinates of the vertices are (h,k±a)
• an elllipse the coordinates of the co-vertices are (h±b,k)
• the length of the major axis is 2a
• the length of the minor axis is 2b
• In the ellipse the coordinates of the foci are (h,k±c), where c​²=a​²​​−b​².

Y-anis Paga ("ь, кча) пло до 10 (6x4) | Яатч) хояј3 minor-anih (h,К-с) Сь, к-а)