Question

Find the point to which the origin should be shifted so that the equation y^2+4y+8x-2=0 is transformed to the form y2 + ax = 0.​

Answer 1

Therefore the origin is shifted to (4,0).

Step-by-step explanation:

Let the origin is shifted to the point (h,k)

If the origin is shifted to the point (h,k) then the new coordinate of (x, y) is (x',y') where x=x'+h , y=y'+k.

The given equation is

$y^2+4y+8x-2=0$

Since the origin is shifted to (h,k).

So putting  x=x'+h , y=y'+k.

$(y'+k)^2+4(y'+k)+8(x'+h)-2=0$

$\Rightarrow y'2+2y'k+k^2+4y'+4k+8x'+8h-2=0$

Putting x'=x and y'=y

$\Rightarrow y^2+2yk+k^2+4y+4k+8x+8h-2=0$

Comparing the above equation with the given equation $y^2+ax=0$

equating the coefficient of y

∴2k=0

⇒k=0

Equating the constant term

k²+4k+8h-2 =0

⇒8h=2    [∵k=0]

⇒h=4

Therefore the origin is shifted to (4,0).

Answer 2

Answer:

(3/4,-2)

Step-by-step explanation:

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