Question

8. In the given figure, A and B are points on a circle with centre 0. If A(1,3) and B(-2. b) then b = (a) V6 (b) -16 (d) None of these (c) 273​

Answer 1

The value of b is \sqrt{6}

6

Step-by-step explanation:

Given:

\begin{gathered}A(1,3)\\\\B(-2,b)\end{gathered}

A(1,3)

B(−2,b)

If the center is at the origin O(0,0)O(0,0)

The distance between the points is the same from the center of the circle

The distance formula for points (x_1,y_1)(x

1

,y

1

) and (x_2,y_2)(x

2

,y

2

) is \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

(x

2

−x

1

)

2

+(y

2

−y

1

)

2

So we get as:

\begin{gathered}\sqrt{(1)^2+(3)^2}=\sqrt{(-2)^2+(b)^2}\\\\\sqrt{10} =\sqrt{b^2+4}\end{gathered}

(1)

2

+(3)

2

=

(−2)

2

+(b)

2

10

=

b

2

+4

\begin{gathered}b^2+4=10\\\\b^2=6\\\\b=\sqrt{6}\end{gathered}

b

2

+4=10

b

2

=6

b=

6