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# A circle and a straight line are drawn on the same coordinate graph.

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Math Expert
Joined: 02 Sep 2009
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A circle and a straight line are drawn on the same coordinate graph.  [#permalink]

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Updated on: 01 Jul 2016, 09:17
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25% (medium)

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74% (01:14) correct 26% (01:10) wrong based on 167 sessions

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A circle and a straight line are drawn on the same coordinate graph. In how many places do the two graphs intersect?

(1) The equation of the circle is x^2 + y^2 = 25.
(2) The y-intercept of the straight line is 6.

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Originally posted by Bunuel on 01 Jul 2016, 04:24.
Last edited by Vyshak on 01 Jul 2016, 09:17, edited 1 time in total.
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Re: A circle and a straight line are drawn on the same coordinate graph.  [#permalink]

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01 Jul 2016, 09:26
St1: Insufficient as we do not know the equation of the straight line

St2: Insufficient as we do not know the equation of the circle or the straight line

Combining St1 and St2: Still insufficient as we only the equation of the circle

Answer: E
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Re: A circle and a straight line are drawn on the same coordinate graph.  [#permalink]

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01 Jul 2016, 09:27
Answer is E: Neither is sufficient to solve.

(1) The equation of the circle is x^2 + y^2 = 25.
This says this is a circle of radius 5 and centre as origin and nothing about the line. So Eliminate A and D

(2) The y-intercept of the straight line is 6.
This says about the line with y intercept as 6, but not about the slope, so incomplete line information and also nothing about the Circle.

combining 1 and 2 , we know about a circle and an incomplete line, so E.
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Re: A circle and a straight line are drawn on the same coordinate graph.  [#permalink]

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01 Jul 2016, 19:49
E

taking both and had the slope been given it was suff,
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Re: A circle and a straight line are drawn on the same coordinate graph.  [#permalink]

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11 Jul 2016, 18:26
hsbinfy wrote:
E

taking both and had the slope been given it was suff,

Hi hsbinfy,

I understand that both statements are insufficient and the answer to this problem is E. However, can you please explain how would slope help us here? If the slope was given, how can we tell how many places the line would intersect? Maybe I'm overthinking but can we not have two cases even if slope was given:

1. Line is tangent to the circle
2. Line is secant to the circle
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Re: A circle and a straight line are drawn on the same coordinate graph.  [#permalink]

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14 Jul 2016, 18:09
Hello experts,

Can you please confirm my understanding?

I agree that the answer to this problem is E. However, can you please explain if slope help us here? If the slope was given, how can we tell how many places the line would intersect? Maybe I'm overthinking but can we not have two cases even if slope was given:

1. Line is tangent to the circle
2. Line is secant to the circle

Thank you.
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Re: A circle and a straight line are drawn on the same coordinate graph.  [#permalink]

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14 Jul 2016, 21:17
1
Donnie84 wrote:
Hello experts,

Can you please confirm my understanding?

I agree that the answer to this problem is E. However, can you please explain if slope help us here? If the slope was given, how can we tell how many places the line would intersect? Maybe I'm overthinking but can we not have two cases even if slope was given:

1. Line is tangent to the circle
2. Line is secant to the circle

Thank you.

A point and the slope defines a line. So, we would be able to get the equation of the line and answer the question.

Check for more here: math-coordinate-geometry-87652.html
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Re: A circle and a straight line are drawn on the same coordinate graph.  [#permalink]

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15 Jul 2016, 20:07
Thanks Bunuel. It is clear now.
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Re: A circle and a straight line are drawn on the same coordinate graph.  [#permalink]

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19 Jul 2016, 10:56
Bunuel wrote:
A circle and a straight line are drawn on the same coordinate graph. In how many places do the two graphs intersect?

(1) The equation of the circle is x^2 + y^2 = 25.
(2) The y-intercept of the straight line is 6.

A circle and a straight line are drawn on the same coordinate graph. In how many places do the two graphs intersect?

(1) The equation of the circle is x^2 + y^2 = 25.
The origin of the circle is at (0,0) and has a radius of 5.
We don't know anything about the line
INSUFFICIENT

(2) The y-intercept of the straight line is 6.
No information about the circle
INSUFFICIENT

Merging both statement
A circle of radios 5 is drawn a the origin and a line with Y intercept at 6 is drawn. The line has one xy pair as (0,6). what about the slope or other (X,Y) pair.
We don't know if the line is horizontal (Won't meet the circle), vertical (meet the circle at two points) or inclined (might meet the circle at 2 points , one points or no points at all)

INSUFFICIENT.

ANSWER Is E
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Re: A circle and a straight line are drawn on the same coordinate graph.  [#permalink]

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23 Jan 2018, 06:35
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Re: A circle and a straight line are drawn on the same coordinate graph.   [#permalink] 23 Jan 2018, 06:35
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# A circle and a straight line are drawn on the same coordinate graph.

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