Question

If point $A(3,5)$ is located on a circle in the coordinate plane, and the center of the circle is the origin, mark the point which lies outside the circle.

• A. $(1.0,6.0)$
• B. $(1.5,5.5)$
• C. $(2.5,4.5)$
• D. $(4.0,4.0)$
• E. $(5.0,3.0)$

Answer 1

The correct option is A $(1.0,6.0)$

Given that point $A$ lies on circle and origin is center

Therefore the radius of circle is $\sqrt{3^2+5^2}=\sqrt{9+25}=\sqrt{34}$

Now the point lies outside the circle, if the distance between that point to origin is greater than radius of circle.

The distance between $(1,6)$ and origin is $\sqrt{1^2+6^2}=\sqrt{1+36}=\sqrt{37}>\sqrt{3}4$.

Therefore the answer is $(1,6)$