Question

plz its urgent
if a circle touches the x axis at A and B whose centre is (2,3) and radius 5cm find length of the cord and coordinates of Aand B

Answer 1

Here is the solution :

If the circle touches the x - axis at A and B,
Then co-ordinates of A and B of y point will be 0,

So,
Let the point A = (a,0)
Let the point B = (b,0)

We know that radius is same throughout the circle,

So,
Let centre be O,
Where Co-ordinates of O = (2,3),

Now, From the Question,
OA = OB = 5 cm,

Distance between (a,b);(c,d) = √((a-c)²+(b-d)²) ------(Formula)

=> OA = 5 cm = √((a-2)²+(0-3)²)
=> Squaring on both sides,
=> 25 cm² = a² + 4 - 4a + 9
=> 25 - 9 - 4 = a² - 4a,
=> 12 = a² - 4a,
=> a² - 4a - 12 = 0,
=> a² -6a + 2a - 12 = 0,
=> a(a-6) + 2(a-6) = 0,
=> (a-6)(a+2) = 0,
=> a = Either 6 or -2,

Therefore the co-ordinates of A and B are (6,0) and (-2,0),

If A = (6,0) Then B = (-2,0)
If A = (-2,0) Then B = (6,0)
Since we don't know which one's correct !

So for the further answer, Let us consider,
A = (6,0) and B = (-2,0)

Distance between A and B according to the formula is,

|√((6+2)²+(0-0)²)|
=> |√(8)²|
=>| √(64) | = 8 cm,

Therefore : The co-ordinates of A and B are (6,0) and (-2,0) and the distance between them is 8 cm,

Hope you understand, Have a great day !
Thanking you, Bunti 360. !