20. In the diagram below, AD, BE and CF are
straight lines that intersect at G.
(a) Find two pairs of possible yalues ofx and y.
(b) If y is 3 times of x, find the values of x
and y.
F
nd
→D
FC
50°
ro
to y
ЭС
套
А е
B
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Answer:
y
2
+xy−12x
2
=0
⇒y
2
+4xy−3xy−12y
2
=0
⇒y(y+4x)−3x(y+4x)=0
⇒(y+4x)(y−3x)=0
So, y=3x or y=−4x are the two straight lines represented by the given equation.
We consider two cases, the first being when y=3x is common to both.
Then, we get ax
2
+2hx(3x)+b(3x)
2
=0
i.e. ax
2
+6hx
2
+9bx
2
=0
a=−6h−9b=−3(2h+3b)
The second case being line y=−4x is common to both, which gives
ax
2
+2hx(−4x)+b(−4x)
2
=0
i.e. ax
2
−8hx
2
+16bx
2
=0
a=8h−16b=8(h−2b)
Hope its helpful to you
Thank you
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