zz0vlb wrote:

Circle C and line K lie in the XY plane. If circle C is centered at the orgin and has a radius 1, does line K intersect circle C?

(1) The X-Intercept of line k is greater than 1

(2) The slope of line k is -1/10. Let the line is \(y -mx +c =0\)

Now if the distance from the center of circle > radius => Line lie outside circle and does intersect with the line.

Distance = \(\frac{|y1-mx1+c|}{\sqrt{(1+m^2)}}\)

Distance from (0,0) = \(\frac{|0*1-m*0+c|}{\sqrt{(1+m^2)}}\)

= \(\frac{|c|}{\sqrt{(1+m^2)}}\)

Since it depends upon both c and m , thus both the statements individually are not sufficient.

So rule out A B and D

Now take 2nd equation m = -1/10

Distance becomes =\(|c|/\sqrt{{1+\frac{1}{10}^2}}\)

d = \(|c|*\sqrt{\frac{100}{101}}\)

Now c>1, but still we cannot say anything about d as if c > \(\sqrt{\frac{101}{100}}\).

then d>1 else d<1 ( take the case when \(\sqrt{\frac{101}{100}}\) \(> c > 1\)

thus E

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