a circle has its centre at the origin and a radius of root 12 .state wether each of the following point is on,outside or inside the circle(1,-root 17),(3,5),(2,2root 2)

Consider the figure,


1) Here, we need to find that the point 1,-17lie inside the circle, on the circle or outside it.
For this, use the distance formula; r2=x2-x12+y2-y12.
Here, calculate the distance between the origin and the point 1,-17. So,
x1=0x2=1y1=0y2=-17
Substituting the above values in the distance formula, we get
r1=1-02+-17-02 =1+17 =18
As, r1>r, so point 1,-17lies outside the circle.
2) Here, we need to find that the point 3,5lie inside the circle, on the circle or outside it.
For this, use the distance formula; r2=x2-x12+y2-y12.
Here, calculate the distance between the origin and the point 3,5. So,
x1=0x2=3y1=0y2=5
Substituting the above values in the distance formula, we get
r2=3-02+5-02 =9+25 =34
As, r2>r, so point 3,5lies outside the circle.
3) Here, we need to find that the point 2,22lie inside the circle, on the circle or outside it.
For this, use the distance formula; r2=x2-x12+y2-y12.
Here, calculate the distance between the origin and the point 2,22. So,
x1=0x2=2y1=0y2=22
Substituting the above values in the distance formula, we get
r3=2-02+22-02 =4+8 =12
As, r3=r, so point 2,22lies on the circle.

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