VGLA conics

Question 1

4 conics

Answer 1

circle, ellipse, hyperbola, parabola

Question 2

special case conics

Answer 2

degenerate conics

Question 3

parabola definition

Answer 3

the set of all points in a plane that are equidistant from a given fixed point and a fixed line in the plane

Question 4

Standard Equation of Parabolar theorem

Answer 4

The standard equation of a parabolar with focus at the point F(0,p) and directrix y = -p with p>0 is given by
x² = 4py

Question 5

A parabola is symmetric with respect to…

Answer 5

the y axis

Question 6

when p is small for x² = 4py

Answer 6

the parabola is narrow

Question 7

When p is large for x² = 4py

Answer 7

the parabola is wide

Question 8

transformation formula for rotation

Answer 8

x' = xcosθ + ysinθ
y' = ycosθ - xsinθ

Question 9

transformation formula for translation

Answer 9

x' = x-p
y' = y-q

Question 10

The standard equation for a parabola with the directrix in the opposite direction

Answer 10

y² = 4px

Question 11

equation of a parabola with focus at the point F(√2/2p,√2/2p) and directrix y = x-√2p with p>0 is given by

Answer 11

(x-y)² = 4p√2(x+y)

Question 12

How else can the equation of a parabola be written as

Answer 12

ax² + bx + c =y

Question 13

the vertex and axis of a parabola with equation ax² + bx + c =y

Answer 13

P(-b/2a, c- b²/4a)

x = -b/2a

Question 14

tangent to a parabola

Answer 14

yy’ = 2p(x+x’)

Question 15

reflective property of a parabola

Answer 15

The tangent and the normal at a point of a parabola are the bissectors of the angles defined by the line PF, with F the focus, and the line through P parallel to the axis of the parabola

Question 16

parametric equations of a parabola

Answer 16

focus (0,p) and directrix y = -p
x=2pt
y=pt²

Question 17

polar equation of a parabola.

focus(0,0) and directrix y =-p

Answer 17

focus(0,0) and directrix y =-p

r(θ) = p/(1-sinθ)

Question 18

polar equation of a parabola.

focus(0,0) and directrix x =-p

Answer 18

focus(0,0) and directrix x =-p

r(θ) = p/(1-cosθ)