Question

A circle centered at the origin contains the point

Answer 1

Answer:

Yes, the distance from the origin to the point (8,√17) is 9 units.

Step-by-step explanation:

The equation of a circle centered at the origin with radius , r has equation:

${x}^{2} + {y}^{2} = {r}^{2}$

Since the circle passes through (0,-9), the radius is 9 units because (0,-9) is 9 units from the origin.

We substitute the radius to get:

${x}^{2} + {y}^{2} = {9}^{2}$

${x}^{2} + {y}^{2} = 81$

If (8,√17) lies on this circle, then it must satisfy this equation:

${8}^{2} + { (\sqrt{17} )}^{2} = 64 + 17 = 81$

This is True.

This means the distance from (8,√17) is 9 units from the origin.