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Circles, lines and planes! help

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Circles, lines and planes! help

by coolgirl26 » Wed Mar 04, 2009 5:54 pm
I am not understanding why the answers are what they are for these two questions. How do you solve and go about?

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) x intercept of like k is greater than 1

2) slope of line k is -1/10

answer E

In XY coordinate plane, line l and line k intersect at point (4,3)? Is product of slope negative?
1) the product of the x intercepts of line L and K is positive
2) the product of the y intercepts of line L and K is negative

answer :c
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Source: — Data Sufficiency |
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by pakaskwa » Wed Mar 04, 2009 9:36 pm
For first question, it's better to know the equation/expression of circle:
x^2+y^2 = r^2

When the circle is centered at the origin of plane xy, with radius 1, the equation is:
x^2+y^2 = 1

The question is asking if a line is intersecting with a circle. It means it's asking if there're common roots for following 2 equations:
1. x^2+y^2 = 1
2. y = ax+b (equation for line k)

Now we can plug in 2 conditions:
1) x intercept of line k is greater than 1. It means: for line k, when y=0, x>0. But we don't know intersect b (if x=0, y=?). So it's insufficient.

2) slope of line k is -1/10
Plug into line k equation, we got y=(-1/10)x+b. Without knowing intersect b, we still don't know if it will intersect with the circle.

Putting 2 conditions together is not sufficient either. So answer is E.
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by pakaskwa » Wed Mar 04, 2009 10:16 pm
For question 2, first I used 2 expressions for line L and K:
L=mx+a
K=nx+b
(m, n are slopes; a, b are intersects)
Question is asking if mn<0.

Stmt 1 can be translated into: when y=0, product of value x from each equation is positive:
mx+a=0
nx+b=0
--> -a/m x -b/n = ab/mn >0
We don't know if mn<0. Insufficient.

Stmt 2 can be translated: when x=0, product of value y from each euqation is negative:
ab<0
There's no mn involved. So insufficient.

Put stmt 1 and 2 together:
ab<0
ab/mn>0
So mn<0

Answer is C
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