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

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

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

Thanks Bunuel. It is clear now.

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