vikramjainbus137 wrote:
Bunuel wrote:
violetsplash wrote:
A circle with center O and radius 5 is shown in the xy-plane. Lines that intersect the circle in 2 points include which of the following ?
I. y = -x +1
II. y = 2x + 1
III. y = (1/2)x - 6
a) I only
b) II Only
c) I and II Only
d) I and III only
e) I, II and III
Please see the attached picture
Check the diagram below:
Attachment:
graph.png
Answer: C.
Hi Bunuel, sorry I did not get this around in my head... Could you explain in a bit more detail please?
I am bad with coordinate geometry, these things just dont seem to get into my head
The way Bunuel plotted the points, drew the lines, and got the answer, without having to manually calculate anything was by looking at the
y-intercept and the slope:
I. y= -x + 1 ... AKA y = \(\frac{-1}{1}\)x+ 1
Y int = +1
Slope = \(\frac{-1}{1}\)(slope is the number before "x"... in this case it's -1)
1) draw a point at your y-int of (0,1)
2) starting from your Y-intercept, which in this case is (0,1), you have to RISE -1, RUN 1 ... that's your second point .... then RISE -1, RUN 1 again and that's your third point on the line, and so on... then connect the points and you have your line with slope of -1/1... this line intercepts the given circle at 2 points
II. y= 2x + 1
Y int = +1
Slope = \(\frac{+2}{1}\)
1) Draw a point at (0,1)
2) Starting from (0,1) RISE 2, RUN 1 and so on, like you did for number I above.
III. y = \(\frac{1}{2}\)x - 6
Y int = -6
Slope = \(\frac{+1}{2}\)
1) Draw a point at (0,-6)
2) Starting from (0,-6), RISE 1, RUN 2 and so on
Number III is the only one that doesn't intersect the circle in 2 points... so answer is C.