Question

If a circle with the centre (1, 5) passes through the point (6, -7), the point (-7, -1) lies.

• A. on the circle
• B. inside the circle
• C. outside the circle

Answer 1

The correct option is B inside the circle

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

So, the radius of the circle = Distance between (1, 5) and (6, -7)

The radius of the circle = $\sqrt{(6-1{)}^2+(-7-5{)}^2}$

The radius of the circle = $\sqrt{(5{)}^2+(-12{)}^2}$

The radius of the circle = $\sqrt{25+144}$

​​​​​​​The radius of the circle = $\sqrt{169}$

The radius of the circle = 13 units

Distance between (1, 5) and (-7, -1) = $\sqrt{(-7-1{)}^2+(-1-5{)}^2}$

Distance between (1, 5) and (-7, -1) = $\sqrt{(-8{)}^2+(-6{)}^2}$

Distance between (1, 5) and (-7, -1) = $\sqrt{64+36}$

​​​​​​​Distance between (1, 5) and (-7, -1) = $\sqrt{100}$

Distance between (1, 5) and (-7, -1) = 10 units

So, the distance between (1, 5) and (-7, -1) is less than the radius of the circle.
Hence, point (-7, -1) lies inside the circle.