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If in the above circle, the center is translated 2 units
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06 Sep 2023, 03:31
06 Sep 2023, 03:31
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If in the above circle, the center is translated 2 units right and 4 units down, and the radius is increased by \(2 \sqrt{2}\) units, which of the following is the equation of the resulting circle?
A. \((x – 8)^2 + (y – 8)^2 = 72
\)
B. \((x – 8)^2 + y^2 = 72
\)
C. \((x – 4)^2 + y^2 = 32\)
D. \((x – 6)^2 + (y – 4)^2 = 32
\)
E. \((x + 8)^2 + y^2 = 72\)
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Re: If in the above circle, the center is translated 2 units
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08 Sep 2023, 11:40
08 Sep 2023, 11:40
1
If the center is translated 2 units right and 4 units down, the new center is (8,0).
To find the radius, you need to find the distance between (2,0) a known point on the circle and (6,4). (2,0) creates a 1:1: root 2 special triangle, meaning the radius of the original circle is 4 root 2. 4 root 2 + 2 root 2 is 6 root 2 (the new radius).
The equation for a triangle is (x - h)^2 + (y-k)^2 = r^2. With the new inputs, the new equation would be (x-8)^2 + y^2 = (6 root 2) ^2. 6 root 2 squared is 72. Choice B is correct.
To find the radius, you need to find the distance between (2,0) a known point on the circle and (6,4). (2,0) creates a 1:1: root 2 special triangle, meaning the radius of the original circle is 4 root 2. 4 root 2 + 2 root 2 is 6 root 2 (the new radius).
The equation for a triangle is (x - h)^2 + (y-k)^2 = r^2. With the new inputs, the new equation would be (x-8)^2 + y^2 = (6 root 2) ^2. 6 root 2 squared is 72. Choice B is correct.
gmatclubot
Re: If in the above circle, the center is translated 2 units [#permalink]
08 Sep 2023, 11:40
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