Question

A circle has its centre at the origin and a point P(5,0) lies on it. The point Q(6,8) lies

• A. Inside the circle
• B. Outside the circle
• C. On the circle
• D. On X - axis

Answer 1

The correct option is A Inside the circle

First, we draw a circle and a point from the given information.

$\because$ The distance between two points $(x_1,y_1)\text{and}(x_2,y_2)$ is $\sqrt{(x_2-x_1{)}^2+(y_2-y_1{)}^2}$

$\therefore$ Distance between origin i.e., O(0,0) and P(5,0), $PO=\sqrt{(5-0{)}^2+(0-0^2)}$
$=\sqrt{(x_2-x_1{)}^2+(x_2-y_1{)}^2}$
$=\sqrt{5^2+0^2}=5=\text{Radius of circle}$

$\text{Distance between origin O(0,0) and Q(6,8) OQ is}=\sqrt{(6-0{)}^2+(8-0{)}^2}$
$=\sqrt{(6^2+8^2)}=\sqrt{36+64}=\sqrt{100}=10$
If the distance of any point from the centre is d and
i) d < radius, then the point is inside the circle
ii) d > radius, then the point is on the circle
iii) d = radius, then the point is outside the circle
Here, we see that, OQ > OP
Hence,the point Q(6,8), lies outside the circle.