Question

find the focus, vertex and equation of the directrix and axis of the parabola x=y square-2y+3​

Answer 1

Answer:

x

2

+2y=8x−7

x

2

−8x=−2y−7

x

2

−8x+16=−2y−7+16

(x−4)

2

=−2(y−

2

9

)

Comparing with the standard equation x

2

=4ay

Vertex of the parabola is

x−4=0,y−

2

9

=0

⇒x=4,y=

2

9

(4,

2

9

)

Axis of the parabola is

x−4=0

x=4

Latus rectum of the parabola is ∣4a∣

Here 4a=−2

⇒a=−

2

1

⇒LL

′

=2

Focus of the parabola is

x−4=0,y−

2

9

=−

2

1

⇒x=4,y=4

(4,4)