Question:
A circle touches the line \(2x + y - 10 = 0\) at (3, 4) and passes through the point (1, -2). Then a point that lies on the circle is
A circle touches the line \(2x + y - 10 = 0\) at (3, 4) and passes through the point (1, -2). Then a point that lies on the circle is
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Use geometry: point of contact implies center lies on perpendicular from the point to the tangent.
Updated On: Jun 4, 2025
- (5, 4)
- (4, 5)
- (-5, 4)
- (4, -5)
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The Correct Option is C
Solution and Explanation
The center lies on the normal to the line at the point of contact (3, 4). Line normal to \(2x + y = 10\) is in direction (2, 1). So parametric form of center: \((3 + 2t, 4 + t)\). Use distance from center to (1, -2) = radius to get t, find center and check which point lies on circle.
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