Question

The combined equation of two sides of a triangle is
x2 - 4xy + y2 = 0 and its centroid is (2,4), then the equation of the
third side will be
(1) x = 3
(2) y = 6
(3) x + y = 9
(4) y = x + 3​

Answer 1

ANSWER

x²+4xy+y²=0

Assuming t=xy

t²+4t+1=0

t=2−4±16−4 ⇒t=−2±3

So the equation AO and OB are 

AO:y+(2−3)x=0

OB:y+(2+3)x=0

Slope of line AB is −1 as it is perpendicular to line OT, where T is the orthocenter.

Slope of AO is m=3−2

Line BT will be perpendicular to AO

∴ Slope of BT is 2+3

Line BT intersects BO at B(x,y)≡(21−3,21+3)

Now we know the slope of AB and the point B

Therefore equation of line AB:x+y=1