intercept of line

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gmat009: Master | Next Rank: 500 Posts; Posts: 458; Joined: Sun Aug 31, 2008 10:44 am; Thanked: 3 times; Followed by:1 members

intercept of line

by gmat009 » Thu Nov 13, 2008 11:24 am

CAn someone plz. explain what information do we need to check if a line intersect a circle or not.

Example :-
Circle C and line K lie in the xy plane. If circle C is centered at the origin and has radius 1 , does line K intersect circle C??

(1) The x intercept of line k is greater than 1
(2) The slope of line K is -1/10

In this question what information do we need?

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Source: Beat The GMAT — Data Sufficiency | Thu Nov 13, 2008 11:24 am

logitech: Legendary Member; Posts: 2134; Joined: Mon Oct 20, 2008 11:26 pm; Thanked: 237 times; Followed by:25 members; GMAT Score:730

Re: intercept of line

by logitech » Thu Nov 13, 2008 11:36 am

gmat009 wrote:CAn someone plz. explain what information do we need to check if a line intersect a circle or not.

Example :-
Circle C and line K lie in the xy plane. If circle C is centered at the origin and has radius 1 , does line K intersect circle C??

(1) The x intercept of line k is greater than 1
(2) The slope of line K is -1/10

In this question what information do we need?

Circle equations are given as:

X^2 + Y^2 = (Radius)^2

and a line is described as:

Y = SLOPE X + CONSTANT

so if they intersect there should be at least one X,Y that satisfied the both equation.

And remember you can have one or two points when you draw a line to a circle.

Can you visualize my explanation ?

Going back to the question

1) INSUF , we know that X>1 but how about the slope ?
2) INSUF, we know the slope but where do line intersect X or Y axis

1+2) SUF, we know both

IMO C

LGTCH
---------------------
"DON'T LET ANYONE STEAL YOUR DREAM!"

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gmat009: Master | Next Rank: 500 Posts; Posts: 458; Joined: Sun Aug 31, 2008 10:44 am; Thanked: 3 times; Followed by:1 members

Re: intercept of line

by gmat009 » Thu Nov 13, 2008 11:51 am

logitech wrote:
gmat009 wrote:CAn someone plz. explain what information do we need to check if a line intersect a circle or not.

Example :-
Circle C and line K lie in the xy plane. If circle C is centered at the origin and has radius 1 , does line K intersect circle C??

(1) The x intercept of line k is greater than 1
(2) The slope of line K is -1/10

In this question what information do we need?
Circle equations are given as:

X^2 + Y^2 = (Radius)^2

and a line is described as:

Y = SLOPE X + CONSTANT

so if they intersect there should be at least one X,Y that satisfied the both equation.

And remember you can have one or two points when you draw a line to a circle.

Can you visualize my explanation ?

Going back to the question

1) INSUF , we know that X>1 but how about the slope ?
2) INSUF, we know the slope but where do line intersect X or Y axis

1+2) SUF, we know both

IMO C

Sorry, answer is not C

Quote

logitech: Legendary Member; Posts: 2134; Joined: Mon Oct 20, 2008 11:26 pm; Thanked: 237 times; Followed by:25 members; GMAT Score:730