Question

if the points A( 4,3 )and b (x, y) are the circle with the centre o (2, 4 )with the value of x ( A,B) is a diameter

Answer 1

Answer:

Step-by-step explanation:

A(4,3)&B(x,y) are the points and line segnebt joining them is the diameter of a circle with center O(2,4)

That is O bisects AB

coordinates of O(2=x+4/2,4=y+3/2)

                         (4=x+4,8=y+3)

                         (x=4-4,y=8-3)

                          (x=0,y=5)

Answer 2

O is the centre

So,

AB is to be made the diameter. Thus, it must pass through the centre.

Also,

AO= BO


The coordinates given that :-

A( 4,3)
B(x, y)
O(2,4)

Since,

O is the mid point. Therefore, The ratio in which O divides A and B is 1:1

Now,

Applying the section formula for the case of mid-point :-


$o(2,4) = o( \dfrac{4 + x}{2} , \dfrac{3 + y}{2} ) \\ \\ \\ \frac{4 + x}{2} = 2 \\ \\ 4 + x = 2 \times 2 = 4 \\ \\ x = 4 - 4 = 0 \\ \\ \\ \\ \frac{3 + y}{2} = 4 \\ \\ 3 + y = 4 \times 2 = 8 \\ \\ y = 8 - 3 = 5$



So,

For X= 0 , AB will be the diameter of the circle with centre (2,4).

Thanks!