Circle Touches x-axis at (a,0), y-axis Intercept b — Find (2a, b²)
A circle x²+y²−αx+βy+γ=0 touches the x-axis at (a,0) and cuts a y-axis intercept of length b, lying below the x-axis. Find the ordered pair (2a, b²).
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Three Circles of Radii a, b, c Touch Externally With x-axis as Common Tangent
Three circles of radii a, b, c touch each other externally with the x-axis as a common tangent. Derive the relation between a, b, c using centre coordinates and distance.
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Circle Through A(2,−1), B(3,4), Center on (x−5)²+(y−1)²=13/2, Find r²
Circle C passes through A(2,−1) and B(3,4), AB not a diameter, and its centre lies on (x−5)²+(y−1)²=13/2. Find r² using the perpendicular-bisector property.