Question

The centre of a circle (0,0) and radius 3 units. Position of the point (2,
$\sqrt{5}$
)
1) Lies inside of the circle
2) Lies on the circle
3) does not lies on the circle
4) Lies out side the circle​

Answer 1

Answer:

Given:-

Radius=3 cm

Center of circle=(0,0)

Solution:-

We will find the distance of point(2,√5).

Let it be A(2,√5).

By using distance formula:---

$\sqrt{ {(x1 - x2)}^{2} + {(y1 - y2)}^{2} }$

Here, x1=2

X2=0

and y1=√5

y2=0

then;

$\sqrt{ {(2 - 0)}^{2} + {( \sqrt{5} - 0)}^{2} }$

$\sqrt{( {2})^{2} + { (\sqrt{5}) }^{2} }$

$\sqrt{4 + 5}$

$\sqrt{9}$

$3$

So,distance between the points is 3 units.

And we also know that radius is 3 units.

So,the point (2,√5) lies on the circle.

So,the correct answer is

2)Lies on the circle

Answer 2

Answer:

(2) lies on the circle

Step-by-step explanation:

Given centre is O(0,0).

Equation of circle is

$(x-0)^{2} + (y-0)^{2} = r \\x^{2} + y^{2} = 3^{2}$

Substitute x=2 ,y=$\sqrt{5}$

$(2)^{2} + (\sqrt{5})^{2} = (3)^{2} \\4 + 5 = 9\\9 = 9$

∴ Since it satisfies the equation of circle, the point lies on the circle