Question

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10
8
6
4
2
10 8 64-2
-2
4
6
-8
618
-10
ctrich ar Of EICS
y
2 4 6 8 10
x
Ta OnciC
A circle centered at the origin contains the point
(0, -9). Does (8, √17) also lie on the circle? Explain.
O No, the distance from the center to the point
(8, √17) is not the same as the radius.
O No, the radius of 10 units is different from the
distance from the center to the point
(8, √17).
O Yes, the distance from the origin to the point
(8, √17) is 9 units.
O Yes, the distance from the point (0, -9) to the point
(8, √17) is 9 units.

Answer 1

Approximate value of √17

• ~4+

So the point is (8,4)

As we can see in graph the point is contained by the circle

Hence the distance

• √(0-8)²+(9-4)²
• √8²+5²
• √89

Approximately 9 units

Option D

Answer 2

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

Explanation:

Equation of a circle

`(x-a)^2+(y-b)^2=r^2`

where:

• (a, b) is the center
• r is the radius

Given:

• center = (0, 0)
• r = 9

Substitute the given values into the formula to create the equation of the circle:

`\implies (x-0)^2+(y-0)^2=9^2`

`\implies x^2+y^2=81`

To find if point
`\sf (8, √(17))` lies on the circle, substitute x = 8 into the found equation and solve for y:

`\implies 8^2+y^2=81`

`\implies 64+y^2=81`

`\implies y^2=81-64`

`\implies y^2=17`

`\implies y=√(17)`

As y = √17 when x = 8, this proves that point (8, √17) lies on the circle.

The distance from the origin to any point on the circle is the radius.

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