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15 Dec 2020, 04:45
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C
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The figure above shows the graph of a certain equation in the xy-plane. The graph is a circle with center O and circumference 6π. At how many different values of y does x = –7.5 ?
(A) 0
(B) 1
(C) 2
(D) 4
(E) Infinitely many
Attachment:
2020-12-15_14-17-57.png [ 20.5 KiB | Viewed 1492 times ]
callmeDP
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15 Dec 2020, 05:02
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IMO C. TWO points for y when x = -7.5
Approach, Let radius be R
Circumference is = 6*pie = 2*pie*R => R = 3 units.
Looks at the graph below, as radius is 3, you will have two possible y, when x = -7.5.
Approach, Let radius be R
Circumference is = 6*pie = 2*pie*R => R = 3 units.
Looks at the graph below, as radius is 3, you will have two possible y, when x = -7.5.
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2020-12-15_14-17-57.png [ 20.97 KiB | Viewed 1368 times ]
15 Dec 2020, 06:53
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The number of points depends on the length of the radius. Now -7.5 is 2.5 points away from -5, which is the x co ordinate of the center.
So if the radius is 2, then x = -7.5 will cut 0 points on the circle.
If the radius = 2.5, then x = -7.5 will be a tangent at 1 point on the circle
if the radius is > 2.5, then x = -7.5 will cut 2 points on the circle.
Given that the circumference = 6π = 2πr. Therefore r = 3 which is greater than 2.5
There are 2 possible values of y.
Option C
Arun Kumar
So if the radius is 2, then x = -7.5 will cut 0 points on the circle.
If the radius = 2.5, then x = -7.5 will be a tangent at 1 point on the circle
if the radius is > 2.5, then x = -7.5 will cut 2 points on the circle.
Given that the circumference = 6π = 2πr. Therefore r = 3 which is greater than 2.5
There are 2 possible values of y.
Option C
Arun Kumar
