Find all xintercepts and yintercepts to the equation x2 2xy

Find all x-intercepts and y-intercepts to the equation x^2 + 2xy + 3y^2 - 4x -12 = 0

Solution

given x²+2xy+3y²-4x-12=0

for x intercept , y=0

x²+0+0-4x-12=0

x²-4x-12=0

(x-6)(x+2)=0

x=6,x=-2

x intercepts are (-2,0) and (6,0)

for y intercept ,x =0

0+0+3y²-0-12=0

3y²-12=0

y²=4

y =-2 , y= 2

y intercepts are (0,-2) and (0,2)