Question

which conic is represented by 11x²-20xy+10y²+4x+8y+3=0​

Answer 1

Answer:

Given conic S:2x2−72xy+23y2−4x−28y−48=0

The general equation of a conic section is a second-degree can be written as

f(x,y)=ax2+2hxy+by2+2gx+2fy+c

Here, h=−36,a=2,b=23,g=−2,f=−14,c=−48

△=abc+2fgh−af2−bg2−ch2

=(2)(23)(−48)+2(−14)(−2)(−36)−2(−14)2−23(−2)2−(−48)(−36)2

=−2208−2016−392−92+62208

=59300=0

h2−ab=(−36)2−2×23=1250

i.e. h2−ab>0

So, it represents a hyperbola.

Now, ∂x∂S=4x−72y−4