Question

Help! Rotate the axis to eliminate the xy-term in the equation then write the equation ins standard form. `x^2-4xy+4y^2+5sqrt(5)y+1=0` Help!?

This is different from the other equations; this is the correct one and has not been solved yet.

Answer 1

`1 + 5 X + 10 Y + 5Y^2=0`

Explanation:

Rotating the coordinate system around the origin by an angle `theta` so that

`x = X cos(theta)-Ysin(theta)`
`y = X sin(theta)+Y cos(theta)`

and substituting we have in the conic now in the coordinates `X,Y`

the coefficient of `XY` is `3sin(2theta)-4cos(2theta)` so choosing `theta` such that `3sin(2theta)-4cos(2theta)=0` or `tan(2theta)=4/3` or `theta = 1/2 arctan(4/3)` we will have

`1 + 5 X + 10 Y + 5Y^2=0` which is a parabola.