Question:
A circle touches the \( x \)-axis at \( (9,0) \). If it also touches the straight line \( y = 14 \), then the equation of the circle is
A circle touches the \( x \)-axis at \( (9,0) \). If it also touches the straight line \( y = 14 \), then the equation of the circle is
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If a circle touches two parallel lines, center lies midway and radius is half the distance.
Updated On: Apr 21, 2026
- \( (x-9)^2 + (y-7)^2 = 49 \)
- \( x^2 + (y-7)^2 = 49 \)
- \( (x-9)^2 + y^2 = 49 \)
- \( (x-9)^2 + (y-7)^2 = 81 \)
- \( (x-7)^2 + (y-9)^2 = 49 \)
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The Correct Option is A
Solution and Explanation
Concept:
Center lies midway between two parallel tangents.
Step 1: Interpret given data.
Touches \( x \)-axis at \( (9,0) \Rightarrow \) center lies vertically above it: \[ \text{Center} = (9,r) \]
Step 2: Touches line \( y=14 \).
Distance between tangents: \[ r + r = 14 \Rightarrow 2r = 14 \Rightarrow r = 7 \]
Step 3: Write equation.
Center = \( (9,7) \), radius = 7 \[ (x-9)^2 + (y-7)^2 = 49 \]
Step 1: Interpret given data.
Touches \( x \)-axis at \( (9,0) \Rightarrow \) center lies vertically above it: \[ \text{Center} = (9,r) \]
Step 2: Touches line \( y=14 \).
Distance between tangents: \[ r + r = 14 \Rightarrow 2r = 14 \Rightarrow r = 7 \]
Step 3: Write equation.
Center = \( (9,7) \), radius = 7 \[ (x-9)^2 + (y-7)^2 = 49 \]
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