Sorry the question is correct.....
x2+y2+2xy-6x-2y+3=0
(x+y)2=6x+2y-3
Add
on both under the square rot of square terms i.e.
(x+y+
)
2=x
2+y
2+2xy+2
x+2
y+
2 = 6x+2y-3+2
x+2
y+
2
slope of (x+y+
) X slope of (x(6+2
)+y(2+2
)+
2 -3) = -1
-1 X -(6+2
)/(2+2
) = -1
-6-2
=2+2
4
=-8
=-2
(x+y-2)2 = 2x-2y+1
Multiply and divide
LHS by (1
2+1
2) =2 RHS by (
[ ]
1
2+1
2)=
[ ]2
2 ( (x+y-2) /
2)
2 =
2( (2x-2y+1) /
2)
( (x+y-2) /
2)
2 =
2 ( (x-y+1/2) /
2)
which is of the form Y2=4AX
Focus is obtained by solving: X-A=0 and Y=0
L.R is X-A=0
Tangent at the vertex is X+A=0
Centre is by solving X=0 and Y=0
Focus is (1,1)
Rate me if correct.........
Moderation Team
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