Question

Which one of these points lies on the given circle

O (-2.5, -2.5)
O (1, 3)
O (2, - √5)
O (-√3, -√7)

Answer 1

Explanation:

every point on the circle has the same distance from the center : r (radius).

we can see that radius right there on the x-axis : the distance of (3, 0) to (0, 0) is simply 3. that is our radius.

the distance formula is applied Pythagoras

distance² = (difference in x coordinates)² +

+ (difference in y coordinates)²

distance = sqrt( ... )

so,

(-2.5, - 2.5)

(-2.5 - 0)² + (-2.5 - 0)² = 6.25 + 6.25 = 12.5

that is not 3² = 9, so the point is NOT on the circle.

(1, 3)

(1 - 0)² + (3 - 0)² = 1 + 9 = 10

that is not 3² = 9, so the point is NOT on the circle.

(2, -sqrt(5))

(2 - 0)² + (-sqrt(5) - 0)² = 4 + 5 = 9

that IS 3² = 9, so, the point IS on the circle.

(-sqrt(3), -sqrt(7))

(-sqrt(3) - 0)² + (-sqrt(7) - 0)² = 3 + 7 = 10

that is not 3² = 9, so the point is NOT on the circle.

Answer 2

Considering the points, only point (2, - √5) is in the circle

• (2, - √5)

How to determine the equation the circle

Equation of a circle is given as:

(x - h)² + (y - k)² = r²

Where

r = radius

h and k are coordinates of the center

x and y is the coordinate of point on the circumference

In the figure h = k = 0 and r = 3

x² + y² = 3²

x² + y² = 9

Points on or within the circle should have points that when substituted will not be more ,than 9

(-2.5, -2.5)

(-2.5)² + (-2.5)² = 12.5 (not in the circle)

(1, 3)

(1)² + (3)² = 10 (not in the circle)

(2, - √5)

(2)² + (- √5)² = 9 (this point is in the circle)

(-√3, -√7)

(-√3)² + (-√7)² = 10 (not in the circle)