Question

Use the graph below to write 5 conic section equations that create it. Use Desmos to check if your equations produce this picture. Hint: 3 circles, 1 ellipse and 1 parabola
1.The head(red circle)
2. The Left Eye (Blue Circle)
3. The Right Eye (Green Circle)
4. The Mouth (Purple Ellipse)
5. The Body (Black Parabola)

Answer 1

Answer:

See below for the graph.

Step-by-step explanation:

A circle or ellipse can be defined using the same sort of equation. Here, we have chosen to use the formulation ...

... ((x -a)/p)^2 +((y -b)/q)^2 -1 = 0

This will be the general form of the equation for an ellipse with center (a, b) and semi-axes p and q, in the x- and y-directions, respectively. When the axes are the same length, the ellipse is a circle.

By defining the function ...

... c(a, b, p, q, x, y) = ((x -a)/p)^2 +((y -b)/q)^2 -1

we can use the same function for all of the circles/ellipses in the figure. The parabola has vertex (0, -6) and a vertical scale factor of -1, so it can be formulated using the vertex form:

... y = k(x -a)^2 +b . . . . . for vertex (a, b) and vertical scale factor k.

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The equations

• (x/6)² +(y/6) -1 = 0
• (x+2)² +(y-2)² -1 = 0
• (x-2)² +(y-2)² -1 = 0
• (x/3)² +(y+2)² -1 = 0
• y = -x² -6