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

Answer:

(a) 5 units

Explanation:

Let A be the point on the circle with (3,4) as its coordinates with centre at the orgin.

let O be the centre(here it's orgin with coordinates (0,0))

A=(3,4)

0A=radius=root of 3²+4²=root of 25= 5 units.

(b)(5,0),(-5,0)

Answer 2

Answer:

(a) The radius of the given circle is found to be 5 units

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

Given:

A point on a circle with a centre at the origin = (3,4)

To Find:

(a) the radius.

(b) The coordinates of the points at which the circle cuts the x-axis.

Solution:

As per the data, given point= (3,4)

Suppose, 'P' be the point on the circle with (3,4) as its coordinates with the centre at the origin.

Let x= 3, y=4

And 'O' be the centre of the circle.

We know that the centre of the circle= origin,

Thus, the coordinates of the origin O= (0,0)

• The radius of the circle refers to the distance from the centre of the circle to any point on the circumference.

That means,

• Radius represents the distance between the points (0,0) and (3,4)

As we know,

• The distance from the origin to the point (x,y) can be calculated as $\sqrt{} (x^{2} +y^{2})$ units.

⇒ Radius OP = $\sqrt({3} ^{2} +4^{2})$ units

⇒ Radius OP = $\sqrt({9}+16)$ units

⇒ Radius OA = $\sqrt{25}$ units

⇒ Radius OA = ± 5 units

⇒ Radius OA= 5 Units (Since radius can not be a negative number)

∴  (a) Radius OA= 5 Units

b) The picture attached below can be taken as a reference

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

Thus, the coordinates of the points at which the circle cuts the x-axis are (5,0)

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