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Further maths A LEVEL > Conics > Flashcards

Flashcards in Conics Deck (20):
1

standard equation for a parabola

y^2=4ax

2

new equation when a parabola it has been translated by the vector [c d]

(y-d)^2=4a(x-c)

3

new equation when a parabola is reflected in the line y=x

x^2=4ay

4

new equation when a parabola is stretched parallel to the x-axis by scale factor c

y^2=(4ax)/c

5

new equation when a parabola is stretched parallel to the y-axis by scale factor c

(y/c)^2=(4ax)

6

standard equation for an ellipse

(x^2/a^2)+(y^2/b^2)=1

7

new equation when an ellipse is translated by vector [c d]

((x-c)^2/a^2)+((y-d)^2/b^2)=1

8

new equation when an ellipse is reflected in the line y=x

(y^2/a^2)+(x^2/b^2)=1

9

new equation when an ellipse is stretched parallel to the x-axis scale factor c

((x/c)^2/a^2)+(y^2/b^2)=1
or
(x^2/(a^2*c^2))+(y^2/b^2)=1

10

new equation when an ellipse is stretched parallel to the y-axis scale factor c

(x^2/a^2)+((y/c)^2/b^2)=1
or
(x^2/a^2)+(y^2/(b^2*c^2))=1

11

standard equation for a hyperbola

(x^2/a^2)-(y^2/b^2)=1

12

new equation when a hyperbola is translated by vector [c d]

((x-c)^2/a^2)-((y-d)^2/b^2)=1

13

new equation when a hyperbola is reflected in the line y=x

(y^2/a^2)-(x^2/b^2)=1

14

new equation when a hyperbola is stretched parallel to the x-axis scale factor c

((x/c)^2/a^2)-(y^2/b^2)=1
or
(x^2/(a^2*c^2))-(y^2/b^2)=1

15

new equation when a hyperbola is stretched parallel to the y-axis scale factor c

(x^2/a^2)-((y/c)^2/b^2)=1
or
(x^2/a^2)-(y^2/(b^2*c^2))=1

16

standard equation for a rectangular hyperbola

xy=c^2

17

new equation when a rectangular hyperbola is translated by vector [d e]

(x-d)(y-e)=c^2

18

new equation when a rectangular hyperbola is reflected in the line y=x

xy=c^2
(doesn't change)

19

new equation when a rectangular hyperbola is stretched parallel to the x-axis scale factor d

(x/d)y=c^2
or
(xy)/d=c^2
or
xy=c^2*d

20

new equation when a rectangular hyperbola is stretched parallel to the y-axis scale factor d

x(y/d)=c^2
or
(xy)/d=c^2
or
xy=c^2*d