Question

Find the focus of the parabola whose vertex is at (- 1, 2) and the directrix x + 2y + 1 = 0​

Answer 1

Answer:

Let P(x,y) be any point on the parabola whose focus is S(−1,−2) and the directrix x−2y+3=0.

Draw PM perpendicular to directrix $$x - 2y + 3 = 0$$

Then by definition SP=PM

⇒SP

2

=PM

2

⇒(x+1)

2

+(y+2)

2

=(

1+4

x−2y+3

)

2

⇒5[(x+1)

2

+(y+2)

2

]=(x−2y+3)

2

⇒5(x

2

+y

2

+2x+4y+5)=(x

2

+4y

2

+9−4xy+6x−12y)

⇒4x

2

+y

2

+4xy+4x+32y+16=0 This is the equation of the required parabola