How many points of intersection does line L and the curve : DS Archive
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# How many points of intersection does line L and the curve

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How many points of intersection does line L and the curve [#permalink]

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18 Jan 2007, 07:35
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How many points of intersection does line L and the curve y=x^2+9 have?
1) The slope of the line is 0
2) The line intersects Y axis at (0,3)
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18 Jan 2007, 12:45
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For me (C)

Stat1
The curve has a shape of a "valley". It goes to a minimum at x = 0 (f'(x) = 2*x = 0).

A line with a zero as slope is represented by an equation like this : y = b.

Thus,
o if b < 9, the line has no intersection with the curve
o if b = 9, the line has 1 intersection with the curve
o if b > 9, the line has 2 intersections with the curve

INSUFF.

Stat2
The line passes by (0,3). Thus, the equation of the line is similar to y = a*x + 3.

Thus, depending on a, the number of intersection with the curve could be either 0, 1 or 2.

INSUFF.

Both (1) & (2)
The equation of the line is y = 3. Since the minimum of the curve is equal to 0, there is no intersection between the line and the curve.

SUFF.

Last edited by Fig on 18 Jan 2007, 13:23, edited 1 time in total.
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18 Jan 2007, 13:19
Agreed C. A very good explanation.
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