Parabola

Question 1

Vertex coordinates

Answer 1

X=0,Y=0

Question 2

Directrix of y^2=4ax

Answer 2

X= -a

Question 3

Focus of y^2= 4ax

Answer 3

X = A, Y= 0

Question 4

Lactus rectum (LR) end point:

Answer 4

(a, 2a)
&
(a, -2a)

Question 5

Length of lactus rectum (LLR)

Answer 5

LLR = 4a = coefficient of x

Question 6

Focus of y^2=-4ax

Answer 6

(-a, 0)

Question 7

Directrix of y^2=-4ax

Answer 7

X=a

Question 8

Equation of tangent for Slope form when given point is outside parabola

Answer 8

Y = mx + a/m

Question 9

Equation of tangent for cartesian form (T=0) when (x, y) is on the parabola curve being y^2 = 4ax

Answer 9

Yy1 = 2a (x + x1)

Question 10

Equation of tangent for parametric form when we suppose parametric coordinate ( at^2, 2at )

Answer 10

Y.2at = 2a ( x + at^2 )
Yt = x + at^2

Question 11

Parametric Equation of chord of parabola

It’s slope ?

Answer 11

2x-y (t1 + t2) + 2at1t2=0

Slope: 2 / t1+ t2

Question 12

Chord passing through focus (a, 0) then t2 (location of a point in terms of parametric form) in terms of t1

& location of 2nd point ( coordinate containing t2) in terms of t1

Answer 12

T2= -1/t1

(at^2, -2a/t1)

Question 13

For a right angle triangle in a parabola t1×t2=

Answer 13

-4