Question

(3,4) is a point on a circle with centre at the origin.
(a)
Find its radius.
(b) Write the coordinates of the points where the circle cuts the x-axis.​

Answer 1

Step-by-step explanation:

Given:-

(3,4) is a point on a circle with centre at the origin.

To find:-

(a)Find its radius.

(b) Write the coordinates of the points where the circle cuts the x-axis.

Solution:-

Given point = (3,4)

Let x = 3 and y = 4

The centre of the circle = the origin

Coordinates of the origin = (0,0)

Radius is the distance from the centre of the circle to any point on the Circumference .

Radius = Distance between the points (0,0) and (3,4)

We know that

The distance from the origin to the point (x,y) is

√(x^2+y^2) units

Radius = √[3^2+4^2] units

=>Radius = √(9+16) units

=>Radius = √25 units

=>Radius = ±5 units

Since radius can not be negative

Radius of the given circle = 5 units

b) Refer the above attachment

The circle cuts the x- axis at (5,0)

Answer:-

a) Radius of the given circle is 5 units

b)The coordinates of the points where the circle cuts the x-axis (5,0)

Used formula:-

• Radius is the distance from the centre of the circle to any point on the Circumference .
• Coordinates of the origin = (0,0)
• The distance from the origin to the point (x,y) is √(x^2+y^2) units