Question

if the points A(4,3) and B(x,5) are on the circle with centre O(2,3) then find the value of x

Answer 1

Here point A, B is on the circle with centre O.
Hence OA and OB are radius.
So, OA=OB. Hence OA² = OB²
By using distance formula
OA²= ( (4-2)² + (3-3)²) = 4 +0 =4
OB²= ( (2-x)² + (5-3)²)= 4 - 2x +x² +4 = x² - 2x +8
BUT OA²=OB²
4 = x² - 2x + 8
x² - 2x + 4 = 0
D²=(b²-4ac)
D²=( (-2)² - 4(1)(4)) = - 12
Here D² is negative
So, D²<0 So, no real roots are possible.

Answer 2

Hope the pic is helpful.

Sobs is squaring on both sides