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.

1 Answer
Dec 20, 2016

#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.