(Math) Geometry Formulas + Equations

Question 1

General equation of a circle

Answer 1

(x-h)² + (y-k)² = r² [(h, k) being the center]

Question 2

Area of a circle

Answer 2

πr²

Question 3

Circumference of a circle

Answer 3

π2r or πd [diameter]

Question 4

General equation of an ellipse

Answer 4

(x-h)²/a² + (y-k)²/b² = 1 [a being the horizontal radius, b being the vertical radius, (h, k) being the center]

Question 5

Area of an ellipse

Answer 5

abπ

Question 6

Foci of an ellipse (when a is the major radius)

Answer 6

(h ± √(a² - b²), k)

Question 7

Foci of an ellipse (when b is the major radius)

Answer 7

(h, k ± √(b² - a²))

Question 8

General equation of a horizontal hyperbola

Answer 8

(x-h)²/a² - (y-k)²/b² = 1 [a from the vertices (h ± a, k), b from the co-vertices (h, k ± b), (h, k) being the center]

Question 9

General equation of a vertical hyperbola

Answer 9

(y-k)²/b² - (x-h)²/a² = 1 [a from the co-vertices (h ± a, k), b from the vertices (h, k ± b), (h, k) being the center]

Question 10

Foci of a horizontal hyperbola

Answer 10

(h ± √(a² + b²), k)

Question 11

Foci of a vertical hyperbola

Answer 11

(h, k ± √(a² + b²))