Question

E
Very Short Answer Type R
(a) Find the equation of the parabola wit
at the origin and satisfying the condition
(i) Focus (2, 0); Directrix x = -2 (N.
(ii) Focus (0, -3); Directrix y = 3. (N.
th of latus-rectum​

Answer 1

Focus

:

(

a

,

0

)

=

(

1

2

,

0

)

Vertex

:

(

h

,

k

)

=

(

0

,

0

)

Computing the distance p using the general formula, we have:

p

=

√

(

h

−

a

)

2

+

(

y

−

0

)

2

p

=

√

(

0

−

1

2

)

2

+

(

0

−

0

)

2

p

=

√

(

1

2

)

2

p

=

1

2

Here, we have:

(

y

−

k

)

2

=

4

p

(

x

−

h

)

Substitute given values in the above formula and simplify it.

(

y

−

0

)

2

=

4

⋅

1

2

(

x

−

0

)

y

2

=

2

x

Thus, the equation of the parabola is

y

2

=

2

x

.