nvuppala wrote:

Circle C and line k lie in the xy plane. If circle C is centered at the origin and has radius 1, does link k intersect circle C?

1) X-intercept of line k is greater than 1

2) The slope of line k is -1/10

Can somebody explain for me?

And, I generally get scared of co-ordinate geometry, Can somebody point me to the right material?

Let the equation of the line be \(y=mx+c\)where m is the slope and c is the y intercept. Then, the x intercept of this line is \(-c/m\)

Now, a line would intersect the given circle only if the length of perpendicular from its centre on the given line is less than or equal to the radius.

Length of perpendicular from centre (origin in this case) to the given line is given by \(|c/\sqrt{(1+m^2)}|\) . This comes from the formula for the perpendicular distance of a point from a line.

We need to find if \(|c/\sqrt{(1+m^2)}|\) is less than or equal to 1 (as radius is 1 in this case).

Statement 1 gives -c/m is greater than 1. or c is less than -m. But under given condition \(|c/\sqrt{(1+m^2)}|\) can be greater than or less than one for various values of c and m. So, insufficient

Statement 2 gives, m = -1/10. Here again, \(|c/\sqrt{(1+m^2)}|\) can be less than or more than 1 for various values of c. So, insufficient

Combining 1) and 2) also, we cant ascertain for sure if \(|c/\sqrt{(1+m^2)}|\) would always be less than or equal to 1. So, insufficient.

Hence, Answer is E.