Unit 5

Question 1

Circle

Answer 1

All points equidistant from center (h, k). Standard form (x-h)^2+(y-k)^2=r^2

Question 2

Ellipse

Answer 2

All points where the sum of distances to two foci is constant. Major axis length = 2a, Minor axis length = 2b, c = \sqrta^2-b^2

Question 3

Hyperbola

Answer 3

All points where the difference of distances to two foci is constant. Opens along positive term axis. c = \sqrta^2-b^2

Question 4

Foci (Ellipse)

Answer 4

Two fixed interior points that determine the ellipse shape. Located on the major axis.

Question 5

Vertices (Ellipse)

Answer 5

Endpoints of the major axis. Farthest points from center on the ellipse.

Question 6

Co-vertices (Ellipse)

Answer 6

Endpoints of the minor axis. Closest points to center on ellipse along short direction.

Question 7

Asymtopes (Hyperbola)

Answer 7

Lines the hyperbola approaches but never touches. Form an “X” crossing the center

Question 8

Transverse axis

Answer 8

The axis the hyperbola opens along. Connects foci direction

Question 9

General form (Conic)

Answer 9

A Conic equation that is expanded (not in completed square form)

Question 10

Major axis

Answer 10

The longest diameter of and ellipse; passes through both vertices and the center

Question 11

Minor axis

Answer 11

The shortest diameter of and ellipse; perpendicular to the major axis; passes through both co-vertices and the center

Question 12

Intercepts

Answer 12

Points where the graph crosses axes