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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 1572 times ]
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callmeDP
Joined: 25 Oct 2020
Last visit: 12 Dec 2022
Posts: 69
Status:No one but you matter
Location: India
Schools: Alberta '23 HEC Montreal
Schools: Alberta '23 HEC Montreal
Posts: 69
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.
Attachments
2020-12-15_14-17-57.png [ 20.97 KiB | Viewed 1442 times ]
Posts: 4,849
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
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