Question

find the equation of parabola whose focus is (2,-3) and directrix is 3x-4y+16=0​

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Answer: The equation of the parabola be,

(3x - 4y + 16)/5 = √((x - 2)² + (y + 3)²)

Given a parabola with focus (2 , -3) and the directrix be 3x - 4y + 16 = 0.

Let (x , y) be any point on the parabola,

distance between (x , y) and (2 , -3) be

distance = √((x - 2)² + (y + 3)²)

distance between (x , y) and the directrix 3x - 4y + 16 = 0

distance = (3x - 4y + 16)/√3² + 4²

distance =  (3x - 4y + 16)/5

Now, (3x - 4y + 16)/5 = √((x - 2)² + (y + 3)²)

The equation of the parabola be, (3x - 4y + 16)/5 = √((x - 2)² + (y + 3)²)

To conclude in one sentence, the equation of the parabola be, (3x - 4y + 16)/5 = √((x - 2)² + (y + 3)²)

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