Circle C and line k lie in the xy-plane. If circle C

[jp.jprasanna]

Hi

Option 2 says slope of the line is -1/10,

Please correct me if of the below points / understanding wrong.

1. since the slope of the line is negative we now know that it has to pass through 2 and 4 the quadrant.

2. Slope is -ve and 1/10 so y = 1 and x = 10 so the line pass through (0,1) and (10, 0)

3 .So we can conclude that the line K touches the circle at (0,1) since the radius of the circle is 1 and it doesn't intersect the circle at any point - hence a definite NO? - Please please let know whats wrong with my logic!?

4. Statement 1 is NS because the line could be parallel to x axis so without know the y intercept we can really say....


Cheers
Jp

[jp.jprasanna]

Hi

Option 2 says slope of the line is -1/10,

Please correct me if of the below points / understanding wrong.

1. since the slope of the line is negative we now know that it has to pass through 2 and 4 the quadrant.

2. Slope is -ve and 1/10 so y = 1 and x = 10 so the line pass through (0,1) and (10, 0)

3 .So we can conclude that the line K touches the circle at (0,1) since the radius of the circle is 1 and it doesn't intersect the circle at any point - hence a definite NO? - Please please let know whats wrong with my logic!?

4. Statement 1 is NS because the line could be parallel to x axis so without know the y intercept we can really say....


Cheers
Jp

OK I see the problem now

Since slope is basically a ratio we cant really pin down the point it intersects the x and y axis correct?

Lets say the radius of the circle is 5

All the below have a slope of -1/10 but

x intercept = 5 and y intercept = .5 slope = - 5/.5 = -1/10
intersect with the circle of radius 5

x intercept = 10 and y intercept = 1 slope = = -1/10
intersect with the circle of radius 5

x intercept = 20 and y intercept = 2 slope = -1/10
DOESN'T intersect with the circle of radius 5

So only we have the equation of the line we can determine where exactly it is intersecting with x and y hence the slope... the converse as show above with the slope = -1/10 we cannot really say where the line is passing through

So using the slope we can only say which direction the line is moving! -ve slope will pass thro' 2 and 4 quadrant (can't comment about 1 and 3 unless we are given more info) and vice versa! Or is there anything else we can decipher more from a of a line slope?

Dear Instructors PLEASE HELP!

Cheers
Jp

[jnelson0612]

Correct! Just knowing the slope of the problem does not tell us anything about its actual location on this coordinate plane. If the slope is -1/10, that means that the line moves down 1 for every 10 it moves over. It *may* be passing through this circle, which is centered at the origin, or it may pass through the y intercept much higher or lower. Try drawing this picture and experimenting with where this line can pass through the y intercept. We really have no idea from this problem. Insufficient.

[denis.tolkachev]

Hi,

I had another question on this problem. Why are (i) and (ii) together are not sufficient?

(i) states that the x-intercept of line k is greater than 1. Doesn't (i) and (ii) together mean that k is then defined as y=-1/10x + b, where b is >1.

When i am plugging various numbers for b and x, i get to (x,y) that show me a line that DOES NOT cross the circle, which means that (C) should be sufficient.

What am i missing?

Thank you,

Denis

[tim]

just because some numbers you plug in give you a line that doesn't cross the circle, that doesn't mean ALL numbers give a line that crosses the circle. try b=1/2 for instance. remember, you can't conclude that a statement is sufficient just because *some* numbers you plug in give the same answer to the question..

[gmatwork]

Will a tangent to a circle considered to intersect a circle?

[tim]

yes, but only in one point

[gmatwork]

Thanks!

[RonPurewal]

Thanks!

glad we could help