Question

Which of the following points lie on the circle described by the equation: x^2+(y−5)^2=32?

(a) (4,1)
(b) (−4,1)
(c) (3,6)
(d) All of the above

Answer 1

The point (3,6) lies on the circle described by the equation x^2+(y-5)^2=32

The correct option is c.

Step-by-step explanation:

The equation of the circle is given by x^2 + (y-5)^2 = 32. To determine which points lie on this circle, we substitute the x and y coordinates of each point into the equation and check if it satisfies the equation.

For point (4,1): (4)^2 + (1-5)^2 = 32. This is not true, so (4,1) does not lie on the circle.

For point (-4,1): (-4)^2 + (1-5)^2 = 32. This is not true, so (-4,1) does not lie on the circle.

For point (3,6): (3)^2 + (6-5)^2 = 32. This is true, so (3,6) lies on the circle.

Therefore, the correct answer is (c) (3,6).