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The equation of a circle is (x + 12)2 + (y + 16)2 = (r1)2, and the circle passes through the origin. The equation of the circle then changes to (x – 30)2 + (y – 16)2 = (r2)2, and the circle still passes
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The equation of a circle is (x + 12)2 + (y + 16)2 = (r1)2, and the circle passes through the origin. The equation of the circle then changes to (x – 30)2 + (y – 16)2 = (r2)2, and the circle still passes through the origin. What are the values of r1 and r2?
Mathematics
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Mabounassif
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For an equation to pass through the origin, (0,0) must be a solution of the equation. So, for the first one,
(0, 0) must satisfy the equation and we can solve for the value of r₁ as shown below.
Since the second equation of the circle also passes through the origin, we use the same steps from the first one.
Thus, we have the values for r₁ and r₂ as 20 and 34, respectively.
Answer: r₁ = 20 and r₂ = 34
Amal Kostali Targhi
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Sep 27, 2018
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Amal Kostali Targhi
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