Determine which of the given points are on the graph of the equation.

Question

​Equation: x2+y2=9

​Points: (0,3) (3,0) ( square root of 3, square root of 3)

Which of these points are on the graph of the equation? Select all that apply.

Answer 1

It's a circle, center at the origin and radius sqr9 = 3

(0,3) and (3,0) are the top of the circle and the right side of the circle

0^2 + 3^2 = 9

and

3^2 +0^2 = 9

both points are on the circle and satisfy the equation

(sqr3, sqr3) is not on the circle.

(sqr3)^2 + (sqr3)^2 = 3 + 3 = 6 which does not = 9

(3/sqr2, 3/sqr2)= ((3/2)sqr2, (3/2)sqr2) is on the circle

Answer 2

x² + y² = 9

0² + 3² = 9

0 + 9 = 9

0 = 0

True, so (0,3) is on the graph.

3² + 0² = 9

9 + 0 = 9

0 = 0

True, so (3,0) is on the graph.

(√3)² + (√3)² = 9

3 + 3 = 9

0 = 3

Not true, so (√3, √3) is NOT on the graph.

Answer 3

x² + y² = 9, is the equation of a circle centre (0,0) radius 3.

(so points that are 3 units distant from (0,0))

obviously (0,3) and (3,0) are on the circle

(sqrt (3), sqrt(3)) is distance sqrt (3+3) = sqrt (6) from (0,0) using the distance formula so is not on the circle