Question

find the vertex focus latest rectum directrix of the following parabola x² -y-2x is equal to zero.​

Answer 1

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Find the vertex, axis, focus, directrix, latus rectrum of following parabolas:

x

2

+2y=8x−7

Medium

Solution

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x

2

+2y=8x−7

x

2

−8x=−2y−7

⇒x

2

−2×4×x+42=−2y−7+4

2

⇒(x−4)

2

=−2y−7+16

⇒(x−4)

2

=−2y+9

⇒(x−4)

2

=−2(y−

2

9

) ....(i)

For replacing origin (0,0) at (4,

2

9

), put x−4=X and y−

2

9

=Y

X

2

−2Y⇒X

2

=

2

1

×T ....(ii)

This is of the form X

2

=4ay where a=−

2

1

In parabola X

2

=4ay

Axis X=0, then x−4=0⇒x=4

Vertex (0,0), then

x−4=0⇒x=4

and y−

2

9

=0⇒y=

2

9

Thus vertex is (4,9/2)

Focus (0,−a), then

x−4=0⇒x=4

and y−

2

9

=−

2

1

⇒y=

2

9

−

2

1

=4

Thus focus is (4,4).

Latus rectum =4a=4×

2

1

=2.

Step-by-step explanation:

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