Question

the circle centered at ( 2,3) and radius 5 units intersects x - axis at A and B.find the coordinates of the points A and B. Also find the length of cord AB .

Answer 1

this is your answer
(6,0) or (-2,0)
AB =4

Answer 2

Answer:

The length of cord AB is 8 units.

Step-by-step explanation:

The standard from of a circle is

$(x-h)^2+(y-k)^2=r^2$

where, (h,k) is center and r is radius.

It is given that circle centered at (2,3) and radius 5 units.

The equation of circle is

$(x-2)^2+(y-3)^2=5^2$

To find the x-intercept, substitute y=0.

$(x-2)^2+(0-3)^2=5^2$

$(x-2)^2+9=25$

$(x-2)^2=16$

Square root both sides.

$(x-2)=\pm 4$

$x-2=4\Rightarrow x=6$

$x-2=-4\Rightarrow x=-2$

The x-intercepts are A(-2,0) and B(6,0).

The length of cord AB is

$AB=\sqrt{(6-(-2)^2+(0-0)^2}=8$

Therefore the length of cord AB is 8 units.