Question

7 poin
13. If the points A(4,3) and B(x,5) are on the circle with centre 0(2,3) the value of x
a o
b.3
c. 2
d. 1
​

Answer 1

Answer:

point A(4,3)

point B (X,5)

CENTER O (2,3)

DISTANCE BETWEEN A AND O

\begin{gathered}\sqrt{(4 - 2) {}^{2} + (3 - 3) {}^{2} } \\ \sqrt{(2 {)}^{2} } \\ distance \: between \: a \: and \: b \: is \: \\ 2 \: units\end{gathered}

(4−2)

2

+(3−3)

2

(2)

2

distancebetweenaandbis

2units

distance between B and O is

\begin{gathered}\sqrt{(x - 2) {}^{2} + (5 - 3) {}^{2} } = 2 \\ (x - 2) {}^{2} + (2) {}^{2} = (2) {}^{2} \\ {x}^{2} - 4x + 4 + 4 = 4 \\ {x}^{2} - 4x + 4 = 0 \\ (by \: factorization) \\ {x}^{2} - 2x - 2x + 4 = 0 \\ ............ \\ .....(x - 2)(x - 2) = 0 \\ value \: of \: x \: is \: 2\end{gathered}

(x−2)

2

+(5−3)

2

=2

(x−2)

2

+(2)

2

=(2)

2

x

2

−4x+4+4=4

x

2

−4x+4=0

(byfactorization)

x

2

−2x−2x+4=0

............

.....(x−2)(x−2)=0

valueofxis2