Question

Determine the lines represented by the eouation x^ 2 +2xy+y^ 2 -2x-2y-5=0​

Answer 1

Answer:

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Equation x

2

−2x−2y+5=0 represents

This question has multiple correct options

Medium

Solution

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Correct options are A) and C)

Given conic is, x

2

−2x−2y+5=0

x

2

−2x+1=2y−4

(x−1)

2

=2(y−2)

Shifting origin to (1,2)

X

2

=2Y where X=x−1 and Y=y−2

Clearly this is Parabola. with latus rectum 2 (here a=

2

1 )

Thus vertex of the parabola is X=0,Y=0⇒(x=1,y=2)

And directrix of X

2

=4aY is Y=−a⇒y−2=−

2

1 ⇒y=

2

3

Answer 2

Answer:

Correct options are A) and C)

Given conic is, x

2

−2x−2y+5=0

x

2

−2x+1=2y−4

(x−1)

2

=2(y−2)

Shifting origin to (1,2)

X

2

=2Y where X=x−1 and Y=y−2

Clearly this is Parabola. with latus rectum 2 (here a=1/2