Question

If the 2 parabolas y^2=4x and y^2=(x-k) have a common normal other than x axis then the value of k is

Answer 1

Answer:

Given,

y

2

=4x

4x=y

2

x=

4

y

2

Use the vertex form:

x=a(y−k)

2

+h

to determine the values of a, h and k.

a=

4

1

,k=0,h=0

Since the value of a is positive, the parabola opens right.

Axis of symmetry: x=0

Since parabolas have a common normal, axis of symmetry of prarabola y

2

=(x−k) also must be x=0.

So:

x−k=0

0−k=0

Add k to both sides

0−k+k=0+k

0=k

k=0

Equation of parabola:

y

2

=(x−k)

y

2

=(x−0)

y

2

=x make me Brian list