ii. দিনলিস্তিন
a. 2x = 1 b =
c. " - 3x d, v২৪ |
Answers
Answer:
Given equation is 3x
2
−4xy−2y
2
−3x−2y−1=0
Let (x
1
,y
1
) be a point to which the origin is shifted by translation
Let (X,Y) be the new coordinates of the point (x,y)
∴ the equations of the transformation are x=X+x
1
,y=Y+y
1
Now the transformed equation is
3(X+x
1
)
2
−4(X+x
1
)(Y+y
1
)−2(Y+y
1
)
2
−3(X+x
1
)−2(Y+y
1
)−1=0
⇒3(X
2
+2Xx
1
+x
1
2
)−4(XY+Xy
1
+Yx
1
+x
1
y
1
)−2(Y
2
+y
1
2
+2YY
1
)−3X−x
1
−2Y−2y
1
−1=0
⇒3X
2
+3x
1
2
+6Xx
1
−4Xy
1
−4x
1
Y−4x
1
y
1
−2Y
2
−2y
1
2
+4Yy
1
−3X−3x
1
−2Y−2y
1
−1=0
⇒(3X
2
−4XY−2Y
2
)+(3x
1
2
−2y
1
2
−4x
1
y
1
−3x
1
−2y
1
−1)+2X(3x
1
−2y
1
−
2
3
)+2Y(−2x
1
+2y
1
−1)=0
Solving the first degree terms,we have
3x
1
−2y
1
=
2
3
−2x
1
+2y
1
=1
Adding the above equations, we get
3x
1
−2y
1
−2x
1
+2y
1
=
2
3
+1
⇒x
1
=
2
5
From equation ,−2x
1
+2y
1
=1
⇒2y
1
=1+2x
1
=1+2×
2
5
=1+5=6
⇒y
1
=
2
6
=3
∴(x
1
,y
1
)=(
2
5
,3)
Hence the point is (
2
5
,3)
Step-by-step explanation: