Coordinate Geometry

Question 1

Distance between points A and B

Answer 1

Squareroot((x2-X1)^2+(y2-y1)^2)

Question 2

Midpoint of segment AB

Answer 2

(X1+x2)/2 , (y1+y2)/2.

Question 3

Potential rule for midpoint of the hypotenuse of a right triangle.

Answer 3

All three vertices are equal distance from the midpoint of the hypotenuse of a right triangle.

Question 4

Parabola

Answer 4

Collection of points in the plane, each of which is equidistance from a fixed line.

Question 5

Locus

Answer 5

A curve or other figure formed by all the points satisfying a particular equation of the relation between coordinates.

Question 6

Directrix

Answer 6

A fixed line used to describing a curve or surface. Formula for directrix is y=k-p when graph opens up or down. Formula is x=h-p if the axis opens left or right.

Question 7

Focus

Answer 7

A fixed point. P=1/4a. Focus formula is (h, k+p) if the parabola opens upward or downward. The formula is (h+p, k) if the directrix opens left or right.

Question 8

Standard form of a parabola

Answer 8

(Y-k)^2=4p(x-h) the graph opens upward or downward

(X-h)^2=4p(y-k) if the graph opens left or right.

Question 9

Vertex

Answer 9

A point that is the maximum or minimum of a parabola. It is half the distance from the focus to the directrix.

Question 10

Ellipse formula

Answer 10

(X-h)^2/(a^2) + (y-k)^2/(b^2)

Question 11

Hyperbola formula

Answer 11

(X-h)^2/a^2 - (y-k)^2/b^2