Move the foci [color=#9900ff][i]F[/i][sub]1[/sub][/color]and[color=#9900ff] [i]F[/i][sub]2[/sub][/color] that define the position of the focal axis of the conic, set the length of the [i]major axis[/i] of the conic using the [color=#1551b5][i]mAxis[/i][/color] slider, then move point [i][color=#6aa84f]P[/color][/i] along the circle to build the locus.[br][br]To create the construction:[br][list][*]Plot 2 points,[color=#9900ff][i] F[sub]1[/sub][/i][/color][color=#ff0000] [/color]and [i][color=#9900ff]F[/color][/i][sub][i][color=#9900ff]2[/color][/i] [/sub]that will be the foci of the conic.[br][/*][*]Draw the circle with center [color=#9900ff][i]F[/i][sub]1[/sub][/color] and [color=#1e84cc]radius [i]r[/i] = [i]mAxis[/i][/color][/*][*]Create a point [color=#6aa84f][i]P[/i][/color] on the circle, then draw the perpendicular bisector of segment [i]P[/i][i]F[/i][sub]2[/sub][/*][*]Line [i]P[/i][color=#ff0000][color=#000000][i]F[/i][/color][sub][color=#000000]1[/color] [/sub][/color]intersects the perpendicular bisector at a point [color=#6aa84f][i]L[/i][/color], which is a point of the conic[/*][/list][br]Point [color=#6aa84f][i]P[/i][/color], moving on the circle, creates the locus of points of [color=#38761D][i]L[/i][/color], that is:[br][br]- an [i]ellipse [/i]if [color=#9900ff][i]F[/i][sub]2[/sub][/color] is [i]inside [/i]the circle [i] distance between foci[/i] < [i]axis length[/i] → [i]e[/i] < 1[br][br]- an [i]hyperbola [/i]if [color=#9900ff][i]F[/i][sub]2[/sub][/color][color=#ff0000][sub] [/sub][/color]is [i]outside [/i]the circle [i]   distance between foci[/i] > [i]axis length[/i] → [i]e[/i] > 1[br][br]- a [i]circle[/i] if [color=#9900ff][i]F[/i][sub]1[/sub] ≡[/color][color=#9900ff][i]F[/i][sub]2[/sub] [/color]      [i] distance between foci[/i] = 0 → [i]e[/i] = 0[br][br]([i]e[/i] = [i]eccentricity[/i])

After creating the locus, draw triangle [i]PLF[sub]2[/sub][/i] and answer the following questions: