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In the xy-plane, line L intersects y = x^2 + 2 at how many points?

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In the xy-plane, line L intersects y = x^2 + 2 at how many points?  [#permalink]

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New post 01 Nov 2019, 07:48
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A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

53% (01:36) correct 47% (01:48) wrong based on 62 sessions

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Re: In the xy-plane, line L intersects y = x^2 + 2 at how many points?  [#permalink]

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New post 01 Nov 2019, 08:07
Bunuel wrote:
In the xy-plane, line L intersects y = x^2 + 2 at how many points?

(1) The slope of Line L is 0
(2) The Line passes through (4,5)


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y = x^2 + 2 is a parabola facing upwards with vertex = (0, 2)

(1) The slope of Line L is 0
--> The line is parallel to x-axis and equation of line is y = k, for any number k
--> Many intersections are possible.

Case 1: If k = 1, Equation of line is y = 1 --> no intersections
Case 2: If k = 2, Equation of line is y = 2 --> 1 intersection
Case 3: If k = 3, Equation of line is y = 3 --> 2 intersections
--> Insufficient

(2) The Line passes through (4,5)
Since we do not know the slope of the line, we cannot say exact number of intersections --> Insufficient

Combining (1) & (2),
slope of line is 0 and passes through (4, 5)
--> Equation of line is y = 5
--> Number of intersections = 2 --> Sufficient

IMO Option C
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Re: In the xy-plane, line L intersects y = x^2 + 2 at how many points?  [#permalink]

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New post 01 Nov 2019, 12:01
A line is defined by 1. Slope ( direction ) and 2. a point

Hence C

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Re: In the xy-plane, line L intersects y = x^2 + 2 at how many points?   [#permalink] 01 Nov 2019, 12:01
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In the xy-plane, line L intersects y = x^2 + 2 at how many points?

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