Conics

Question 1

standard equation for a parabola

Answer 1

y^2=4ax

Question 2

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

Answer 2

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

Question 3

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

Answer 3

x^2=4ay

Question 4

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

Answer 4

y^2=(4ax)/c

Question 5

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

Answer 5

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

Question 6

standard equation for an ellipse

Answer 6

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

Question 7

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

Answer 7

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

Question 8

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

Answer 8

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

Question 9

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

Answer 9

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

Question 10

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

Answer 10

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

Question 11

standard equation for a hyperbola

Answer 11

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

Question 12

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

Answer 12

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

Question 13

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

Answer 13

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

Question 14

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

Answer 14

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

Question 15

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

Answer 15

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

Question 16

standard equation for a rectangular hyperbola

Answer 16

xy=c^2

Question 17

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

Answer 17

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

Question 18

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

Answer 18

xy=c^2

doesn’t change

Question 19

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

Answer 19

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

Question 20

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

Answer 20

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