Question

Find the equation of a circle that is centered at the origin and is tangent to the circle (x−6)^2+(y−8)^2=25

Answer 1

Answer:

$x^2 +y^2 = 25$

Step-by-step explanation:

Center of the required circle = (0, 0)

Center of the given circle = (6, 8)

Radius of the given circle = 5 units

Distance between the centers of both the circles

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

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

$=\sqrt{36 +64}$

$=\sqrt{100}$

$=10\: units$

Since, required circle is tangent to the given circle with radius 5 units.

Therefore,

Radius of required circle = 10 - 5 = 5 units

Now, Equation of required circle can be obtained as:

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

$(x)^2 +(y)^2 = 25$

$x^2 +y^2 = 25$

Answer 2

 

Center:  ( 6 , 8 )

Radius: 5