Question

What is the equation for the parabola that has a focus at (-7, 6) and a directrix of x 1?

Answer 1

Answer:

Step-by-step explanation:

Parabola's equation is

y

=

1

16

(

x

−

7

)

2

+

1

and vertex is

(

7

,

1

)

.

Explanation:

Parabola is locus of a point which moves so that its distance from a given point calld focus and a given line ccalled directrix is always constant.

Let the point be

(

x

,

y

)

. Here focus is

(

7

,

5

)

and distance from focus is

√

(

x

−

7

)

2

+

(

y

−

5

)

2

. Its distance from directrix

y

=

−

3

i.e.

y

+

3

=

0

is

|

y

+

3

|

.

Hence equaion of parabola is

(

x

−

7

)

2

+

(

y

−

5

)

2

)

=

|

y

+

3

|

2

or

x

2

−

14

x

+

49

+

y

2

−

10

y

+

25

=

y

2

+

6

y

+

9

or

x

2

−

14

x

+

65

=

16

y

i.e.

y

=

1

16

(

x

2

−

14

x

+

49

−

49

)

+

65

16

or

y

=

1

16

(

x

−

7

)

2

+

65

−

49

16

or

y

=

1

16

(

x

−

7

)

2

+

1

Hence parabola's equation is

y

=

1

16

(

x

−

7

)

2

+

1

and vertex is

(

7

,

1

)

.

graph{(1/16(x-7)^2+1-y)((x-7)^2+(y-1)^2-0.15)((x-7)^2+(y-5)^2-0.15)(y+3)=0 [-12.08, 27.92, -7.36, 12.64]}