Could you please help me with the approach for this question.
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?
I. The x-intercept of line k is greater than 1.
II. The slope of line k is –(1/10).
Hi Ryan,
Best way to solve this question is plotting it and visualizing it.
Given that, Circle C is centered at the origin and has radius 1.
Question: Does line k intersect the given circle ?
Statement I is insufficient:
x-intercept of line k greater than 1.
x-intercept means the line where it cuts the x-axis.
This doesn’t help anything, it may or may not intersect the circle.
Say if the line is x = 5, it may not intersect the circle.
but we could also draw a line which intersects circle and x intercept greater than 1. If you plot the point (1.5,0) and (0,0.5) , you could see that.
Statement II is insufficient:
Slope of the line is negative – (1/10).
its means for every 1 unit drop in Y, we are moving ten units in X.
we don’t know which quadrant it pass through, it may or may not intersect circle C. we don’t the intercepts too.
Again, this is not sufficient.
Together still not sufficient.
Say if we take the points on the line as,
(0, 2.5 ) and (2.5, 0) then it will intersect the Circle
But if we take points,
(0,3) and (30,0), then it may not intersect the circle
So insufficient.
Answer has to be E.
Just plot the above points, you will get a better clarity.
Hope this helps.