At how many points does line L intersect with the parabola

Smita04 · **Posted:** Wed Feb 01, 2012 7:16 pm


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At how many points does line L intersect with the parabola represented by y = x² - 3x + 6?
(1) Line L is parallel to x-axis.
(2) Line L passes through the point (0, 16).

Apex231 · **Posted:** Wed Feb 01, 2012 9:44 pm

At how many points does line L intersect with the parabola represented by y = x² - 3x + 6?

y = x² - 3x + 6?

Since a (coefficient of x²) is +ve, it's an upward parabola.

y intercept is 6

(1) Line L is parallel to x-axis.
Not sufficient, as we don't know where does it intersects the y axis.

(2) Line L passes through the point (0, 16).
Not sufficient as we don't know the slope, depending on slope line may intersect parabola at zero or multiple points.

(1) + (2)

Sufficient, lines intersects parabola at only two points i.e. where y = 16.

C

amit2k9 · **Posted:** Thu Feb 02, 2012 1:26 am

a. means y=0,substituting in the equation we get two values for x.
sufficient.

b y= mx + c meaning y = 0+ 16 (substitution)
clearly no clue about other point and slope.
Not sufficient.

A it is.

bb · **Posted:** Thu Feb 02, 2012 1:31 am

Smita04 wrote:

At how many points does line L intersect with the parabola represented by y = x² - 3x + 6?
(1) Line L is parallel to x-axis.
(2) Line L passes through the point (0, 16).

What is the source? You did not specify....

saikarthikreddy · **Posted:** Thu Feb 02, 2012 3:52 am

Both Statements 1 and 2 are required

Bunuel · **Posted:** Thu Feb 02, 2012 9:19 am

At how many points does line L intersect with the parabola represented by y = x² - 3x + 6?

Generally a parabola and a line can have 0, 1, or 2 intersection points.

Notice than in our case, since the coefficient of x^2 is positive, then we have an upward parabola, which intersects y-axis at (0, 6). Just to illustrate, below is the graph of y = x^2 - 3x + 6:

Attachment:

parabola.gif [ 3.02 KiB | Viewed 389 times ]

(1) Line L is parallel to x-axis. All three cases are possible: line L can be below the given parabola (no intersection), line L can go through the vertex (1 intersection) or cross it above the vertex (2 intersections). Not sufficient.

Notice that if it were: line L is parallel to y-axis then we would know that it would cross a parabola at one point, hence in this case the statement would be sufficient.

(2) Line L passes through the point (0, 16). Since (0, 16) is higher than y-intercept of parabola, then line L is "trapped" and must have at least one intersection with parabola (it'll have only one for example if L is y=0). Not sufficient.

(1)+(2) Line L intersect with the parabola at two points. Sufficient.

Answer: C.

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At how many points does line L intersect with the parabola

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