Question

The directric ofa parabola with focus (5,6) and vertex (3,8)
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Answer 1

Step-by-step explanation:

Correct option is

B

x-y+5=0

Given:-

Vertex ≡(3,6)

Focus ≡(4,5)

Equation of axis of symmetry-

(y−6)=

4−3

5−6

(x−3)

y−6=−x+3

⇒x+y−9=0

⇒ slope of axis of symmetry =−1

Therefore, slope of directrix =1

As we know that in a parabola, vertex is the mid-point of of focus and the point of intersection of directrix and axis of symmetry.

Now,

Let co-ordinate of the point of intersection of direction and axis of symmetriy be (a,b) then

2

a+4

=3

⇒a+4=6

⇒a=6−4=2

2

b+5

=6

⇒b+5=12

⇒b=12−5=7

Thus the point of intersection is (2,7).

Therefore,

Equation of directrix will be-

(y−7)=1(x−2)

⇒x−y+5=0

Hence the equation of directrix is x−y+5=0.

Hence the correct answer is (B)x−y+5=0.

Answer 2

Step-by-step explanation:

Given:-

Vertex ≡(3,8)

Focus ≡(5,6)

Equation of axis of symmetry-

(y−8)= {(6−8)/(5−3)}(x−3)

y−8=−x+3

⇒x+y−11=0

⇒ slope of axis of symmetry =−1

Therefore, slope of directrix =1

As we know that in a parabola, vertex is the mid-point of of focus and the point of intersection of directrix and axis of symmetry.

Now,

Let co-ordinate of the point of intersection of direction and axis of symmetriy be (a,b) then

(a+5)/2 =3

⇒a+5=6

⇒a=6−5=1

(b+6)/2=8

⇒b+6=16

⇒b=16−6=10

Thus the point of intersection is (1,10).

Therefore,

Equation of directrix will be-

(y−10)=1(x−1)

⇒x−y+9=0

Hence the equation of directrix is x−y+9=0.

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