Question

Weite the equation of the parabola which
has focus
the origin
on origin y-x = 4

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Answer 1

Answer:

REF.Image.

Given parabola y=x

vertex distance 2 from origin

Let vertex =(1,1) a b

focus distance 2 ,2 from origin

focus =(2,2) h k

Equation of directrix →x+y=0

Equation of parabola

(x+h) 2 +(y−k) 2

= a 2 +b 2

ax+by+c(x−2) 2 +(y−2) 2

=( 2x+y) 2

2[x 2+y 2 +4+4−4x−4y]=(x+y) 2

2x 2 +y 2 −8x−8y+16=x

2 +y 2+2xyx 2 +y 2

−2xy=8x+8y−16(x−y) 2

=8(x+y−2)