Question

Find the equation of the cone reciprocal to the cone

fyz + gzx+ hxy = 0​

Answer 1

Answer:

yes correct answer okkk

Answer 2

Step-by-step explanation:

given cone ayz+bzx+cxy=0,ayz+bzx+cxy=0, the actual reciprocal cone is

a2x2+b2y2+c2z2−2bcyz−2cazx−2abxy=0.a2x2+b2y2+c2z2−2bcyz−2cazx−2abxy=0.

About the coordinate planes, what happens when z=0?z=0? Then

a2x2−2abxy+b2y2=(ax−by)2=0,a2x2−2abxy+b2y2=(ax−by)2=0,

so that

ax=by.ax=by.

This is a single line, therefore the cone is tangent to the plane z=0.z=0. Another way to confirm tangency is to point out that a point on this line is, for some t,t, given by (bt,at,0).(bt,at,0). Furthermore, for a quadratic form given by vtHv,vtHv, the gradient is given ( as a column vector) by 2Hv.2Hv. We then calculate