Question

In the given figure, which of the following points lies within the circle?

• A. $(3.5,9.5)$
• B. $(-7,7)$
• C. $(-10,1)$
• D. $(-10,-1)$

Answer 1

The correct option is B $(-7,7)$

The centre of the circle is at $(0,0)$.

$\therefore$ Its equation is $x^2+y^2=r^2$ ......(i)

When $r=$ radious of the circle.

It passas through $(6,8)$.

$\therefore$ putting $x=6$ and $y=8$ in (i), we get

$6^2+8^2=r^2⟹r=10$ units.

If the distance of any point is less than the length of the radius $r$, then it will be within the circle.

Now, we investigate each option which has a point at a distance $=d$ less than the length of $r$.

Option A: $⟶x_1=3.5,y_1=9.5$

${\therefore d}^2={x_1}^2+{y_1}^2={3.5}^2+{9.5}^2=102.5⟹d>10$

Option B: $⟶x_1=-7,y_1=7$

${\therefore d}^2={x_1}^2+{y_1}^2=({-7)}^2+7^2=93.50⟹d<10$

Option C: $⟶x_1=-10,y_1=1$

${\therefore d}^2={x_1}^2+{y_1}^2=({-10)}^2+1^2=101.1⟹d>10$

Option D: $⟶x_1=-10,y_1=-1{\therefore d}^2={x_1}^2+{y_1}^2=({-10)}^2+(-{1)}^2=101.1⟹d>10$

$\therefore$ Only $(-7,7)$ lies within the circle.