Math, asked by hero87923, 10 months ago

If you do not answer or write the answer for points please guys
Find the equation of parabola whose vertex is (-1,1) and directrix is 4x+3y-24=0

Answers

Answered by madhunacha
1

Answer:

Length of latus rectum is twice the distance between focus and vertex or four times the distance of focus from directrix.

The distance of focus

(

1

,

1

)

from directrix

4

x

+

3

y

24

=

0

is

4

×

(

1

)

+

3

×

1

24

4

2

+

3

2

=

4

+

3

24

5

=

25

5

=

5

Hence, length of latus rectum is

10

.

As parabola is locus of a point, which moves so that its distance from focus and directrix is alwaays equal, its equation is

4

x

+

3

y

24

4

2

+

3

2

2

=

(

x

+

1

)

2

+

(

y

1

)

2

or

16

x

2

+

9

y

2

+

576

+

24

x

y

192

x

144

y

=

25

x

2

+

50

x

+

25

+

25

y

2

50

y

+

25

or

9

x

2

+

16

y

2

24

x

y

+

242

x

+

94

y

526

=

0

Ends of latus rectum are

(

4

,

5

)

and

(

2

,

3

)

graph{(9x^2+16y^2-24xy+242x+94y-526)((x+1)^2+(y-1)^2-0.08)((x+4)^2+(y-5)^2-0.08)((x-2)^2+(y+3)^2-0.08)(4x+3y-24)(4x+3y+1)=0 [-10.42, 9.58, -4.16, 5.84]}

Answered by licraushan
0

Answer:

10 is the correct answer

Step-by-step explanation:

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