Question:
If a circle S passes through the origin and makes intercept 4 units on line \(x = 2\), then the equation of curve on which center of S lies is
If a circle S passes through the origin and makes intercept 4 units on line \(x = 2\), then the equation of curve on which center of S lies is
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Use standard form and geometric constraints to express locus as a curve equation.
Updated On: Jun 4, 2025
- \(y^2 - 4x = 8\)
- \(y^2 + 4x = 8\)
- \(x^2 + 4y = 8\)
- \(x^2 - 4y = 8\)
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The Correct Option is B
Solution and Explanation
Let circle have center at \((a, b)\) and radius \(r\). Since it passes through origin:
\[
a^2 + b^2 = r^2
\]
And intercept on line \(x = 2\) is 4 units \Rightarrow vertical length of chord = 4
Use perpendicular distance from center to line = \(\sqrt{r^2 - d^2}\) or compute using geometry. Final equation: \(y^2 + 4x = 8\)
Use perpendicular distance from center to line = \(\sqrt{r^2 - d^2}\) or compute using geometry. Final equation: \(y^2 + 4x = 8\)
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