danjuma wrote: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?
1.The X-intercept of line K is greater than 1
2.The slope of line K is -1/10
IOM Answer C.
To determine whether line K intersects circle C we need the equation of the line for K and general equation for circle (x-a)^2+(y-b)^2=R^2 [a,b=0 origin, R=1). To find the equation, we need either two points, or one point and the slope. Both statements, on their own, are insufficient, as they provides only one point and the slope.
Taken together, two statements are sufficient: with one point, and the slope we can find the equation of line k. With the equation of the line K, we can answer the question.
y=ax+b, st(1) y=a*(x>1, say 11/10) + b, x intercept condition y=0 ____ 0=a*(x>1) + b
st(2) y=-1/10*x + b
st(1&2) y=-1/10*(x>1, x=11/10) + b; x intercept condition y=0 _____0=-1/10*(x>1, x=11/10) + b, b=11/10 (y intercept) because x=y E {-1;1} b=11/10 means that line K does not intersect the circle C. To test - plug in R {0;1 and 1;0} into line equation.
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