Question

Find the focus, length of latus rectum and the equation of the parabola whose vertex is (-1,-1) and directrix x+ y+ 4 = 0

Answer 1

Answer:

focus = (1,1)

eq  

n

directrix =x+y+1=0

Let A(x,y) be the pt. on the parabola

& AM be the length of ⊥ from A to

directrix

Then SA = AM

⇒(SA)  

2

=(AM)  

2

 

⇒(x−1)  

2

+(y−1  

2

)=  

(  

1  

2

+1  

2

 

​  

)  

2

 

(x+y+1)  

2

 

​  

 

⇒x  

2

+1−2x+y  

2

+1−2y=  

2

x  

2

+y  

2

+1+2xy+2y+2x

​  

 

⇒2x  

2

+2−4x+2y  

2

+2−4y=x  

2

+y  

2

+1+2xy+2x+2y

⇒x  

2

+y  

2

−6x−6y−2xy+3=0 mark me as brainliest

Step-by-step explanation: