Find the co-ordinates of the point on transferring the origin to which the equation
x2 + 3x y + 4y - 4x-6y + 5 = 0 does not contain linear terms in x and y. Also
find the new equation.
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Answer:
please mark as brainlist answer
Step-by-step explanation:
Let the origin be shifted to the point (h,k).
Let (x,y) and (x
′
,y
′
) are the coordinates of a point in the old and new system respectively, then x=x
′
+h,y=y
′
+k.
So, the transformed equation is
14(x
′
+h)
2
−4(x
′
+h)(y
′
+k)+11(y
′
+k)
2
−36(x
′
+h)+48(y
′
+k)+41=0
⇒14x
′
2
+28x
′
h+14h
2
−4x
′
y
′
−4x
′
k−4y
′
h−4hk+11y
′
2
+11k
2
+22y
′
k−36x
′
−36h+48y
′
+48k+41=0
⇒14x
′
2
+11y
′
2
+x
′
(28h−4k−36)+y
′
(−4h+22k+48)
+(14h
2
−4hk−36h+48k+41)−4x
′
y
′
=0
In order to remove the first degree term, we must have
28h−4k−36=0 and −4h+22k+48=0
⇒h=1 and k=−2
∴ the origin must be shifted to the point (1,−2) to remove the 1
st
degree terms from the given equation.
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