What is the graph of xy = 3y?

Ans. (E) a right angle.

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EDIT :

For a Multiple Choice Question, the option which

is broadest in meaning is given the credit when only

one option is to be chosen.

The equation xy = 3y, i.e., y(x-3) = 0 does represent 2 lines

having separate equations y = 0 and x = 3. But that is only

the basic import of the question.

Since the line y=0 ( X-axis, a horizontalal line ) and the line

x = 3 ( parallel to Y-axis, a vertical line ) are at right

angles, it stands to reason that, in addition to being two

lines, they have something more : that they can be viewed

as being the two Arms of a Right Angle whose Vertex is at

the point ( 3, 0 ).

Hence, a broader interpretation of the equation xy = 3y

is given by the option : (E) a right angle.

So no matter how many TDs I am given,

I stand by my answer.

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P.S. : Although I don't ' administer ' TDs,

. . . . I have always been at the receiving end.

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EDIT - 2

[ If we are going to be so analytical mathematically,

then I will be equally analytical linguistically. ]

Of course, I was aware of the 4 right angles.

I also noted the indefinite article ' a ' in option (E)

which said " ' a ' right angle ", indicating 'any' one of the

four.

If it had said " ' the ' right angle ", then the option would

have been wrong.

As the things stand, I too remain convinced that

" ' a ' right angle " is the Most Correct of the options given.

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I don't know why previous answers of 2 lines have got thumbs down because they are correct.

xy = 3y ----> y = 0 or x = 3

EDIT. Comment to Hemant. A right-angle would imply two half lines or rays emanating from a point. It is true that the two lines in my answer are perpendicular, but one could argue that they make four right-angles at their intersection.

I remain convinced that two lines is the most correct of the options given.

EDIT 2. O.K. Let's agree to disagree.

take the derivative: 3x^2dx + y^2dx + 2xydy - 3dy = 0\ solve for dy/dx: (3x^2 + y^2)dx + (2xy - 3)dy = 0 dy/dx = - (3x^2 + y^2) / (2xy - 3) substitute in (2,-1): dy/dx = - (12 + 1) / (-4 - 3) dy/dx = 13/7 equation of the tangent line in point slope form: y + 1 = 13/7 (x - 2)

D

y=1/(x-3)

has asymptote but is 2 lines

D: two lines (which happen to intersect at right angle).

c

(C) one line

D

(C)