Solve for y in terms of x then solve for some (x, y) coordinates to draw its graph
Using quadratic formula
rewrite the equation first, so that it appears as follows
y^2+sqrt3xy+2x^2-10=0y2+√3xy+2x2−10=0
Let a=1a=1 and b=sqrt3xb=√3x and c=2x^2-10c=2x2−10
y=(-b+-sqrt(b^2-4ac))/(2a)y=−b±√b2−4ac2a
y=(-sqrt3x+-sqrt((sqrt3x)^2-4(1)(2x^2-10)))/(2*1)y=−√3x±√(√3x)2−4(1)(2x2−10)2⋅1
y=(-sqrt3x+-sqrt(40-5x^2))/2y=−√3x±√40−5x22
Compute y values for some x arbitrary values
y=(-sqrt3x+sqrt(40-5x^2))/2y=−√3x+√40−5x22
" "x" " " " " " "y x y
" "0" " " " "+3.16 0 +3.16
+0.5" " " " "2.679+0.5 2.679
+0.75" " " " "2.399+0.75 2.399
+1" " " " "2.092+1 2.092
+1.25" " " " "1.754+1.25 1.754
+1.5" " " " "1.3819+1.5 1.3819
+1.75" " " " ".9687+1.75 .9687
+2" " " " "0.504+2 0.504
+2.25" " " " "-0.0323+2.25 −0.0323
+2.5" " " " "-0.68604+2.5 −0.68604
+sqrt3" " " " "1+√3 1
" "x" " " " " " "y x y
-0.5" " " " "3.54548−0.5 3.54548
-0.75" " " " "3.698−0.75 3.698
-1" " " " "3.824−1 3.824
-1.25" " " " "3.919−1.25 3.919
-1.5" " " " "3.9799−1.5 3.9799
-1.75" " " " "3.9998−1.75 3.9998
-2" " " " "3.968−2 3.968
-2.25" " " " "3.864−2.25 3.864
-2.5" " " " "3.644−2.5 3.644
-sqrt3" " " " "4−√3 4
Kindly see the graph of y^2+sqrt3xy+2x^2-10=0y2+√3xy+2x2−10=0
graph{y^2+sqrt3xy+2x^2-10=0[-sqrt8,sqrt8,-5,5]}
God bless you...
