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Normal to a Circle
A normal to a circle is a line that intersects the circle at a right angle, also known as a perpendicular line. The normal to a circle at a certain point is the line that passes through that point and is perpendicular to the tangent line at that point.
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Finding the Normal
To find the normal to the circle (x-1)^2 + (y-2)^2 = 10, we need to find the gradient of the circle at a specific point. The gradient of the circle is the negative reciprocal of the gradient of the tangent at that point.
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Comparing Options
Let's compare the given options to see which one is normal to the circle:
(A) X+Y=3: This is a linear equation and not necessarily a normal to the circle.
(B) (x-1)+(y-2)=10: This equation is not in the form of a line and does not represent a normal to the circle.
(C) X+2Y=0: This equation is a linear equation, but it does not pass through the center of the circle and is not necessarily a normal.
(D) 2X+Y=3: This equation is a linear equation and does not pass through the center of the circle, so it is not a normal to the circle either.
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Conclusion
None of the given options (A), (B), (C), or (D) represent a line that is normal to the circle (x-1)^2 + (y-2)^2 = 10. To find the normal to the circle, you would need to find the gradient of the circle at a specific point and determine the line that is perpendicular to the tangent at that point.