Question:
If two circles \( (x - 1)^2 + (y - 3)^2 = r^2 \) and \( x^2 + y^2 - 8x + 2y + 8 = 0 \) are given, then
If two circles \( (x - 1)^2 + (y - 3)^2 = r^2 \) and \( x^2 + y^2 - 8x + 2y + 8 = 0 \) are given, then
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To find the relationship between two circles, simplify the equations and compare the centers and radii.
Updated On: Apr 15, 2025
- \( 2 < r < 8 \)
- \( r < 2 \)
- \( r = 2 \)
- \( r > 2 \)
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The Correct Option is A
Solution and Explanation
We are given two equations of circles: 1. \( (x - 1)^2 + (y - 3)^2 = r^2 \), which represents a circle with center \( (1, 3) \). 2. \( x^2 + y^2 - 8x + 2y + 8 = 0 \), which we simplify to find the equation of the second circle. After simplifying the second circle's equation, we find the radius \( r \), and based on the relationship, the final result gives \( 2 < r < 8 \).
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