If a circle is centered at (0, 0) with a radius of 5, which of the following poi

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Question: If a circle is centered at (0, 0) with a radius of 5, which of the following points lies outside the circle?

Options:

Correct Answer: (6, 0)

Solution:

The equation of the circle is x² + y² = 25. The point (6, 0) gives 6² + 0² = 36, which is greater than 25, hence it lies outside.

If a circle is centered at (0, 0) with a radius of 5, which of the following points lies outside the circle?

If a circle is centered at (0, 0) with a radius of 5, which of the following points lies outside the circle?

Step 1: Understand that the center of the circle is at the point (0, 0).
Step 2: Know that the radius of the circle is 5.
Step 3: Use the formula for the equation of a circle, which is x² + y² = r², where r is the radius.
Step 4: Since the radius is 5, calculate r²: 5² = 25. So, the equation of the circle is x² + y² = 25.
Step 5: To find out if a point lies inside or outside the circle, plug the x and y coordinates of the point into the equation x² + y².
Step 6: If the result is greater than 25, the point is outside the circle. If it is less than 25, the point is inside the circle.
Step 7: For the point (6, 0), calculate: 6² + 0² = 36.
Step 8: Compare 36 with 25. Since 36 is greater than 25, the point (6, 0) lies outside the circle.

Circle Equation – Understanding the standard form of a circle's equation and how to determine the position of points relative to the circle.
Distance from Center – Calculating the distance of a point from the center of the circle to determine if it lies inside, on, or outside the circle.