Question

The center of a circle is on the line y =2x and the line x=1 is tangent to the circle at (1, 6).

Find the center and radius of the circle. ​

Answer 1

Answer:

x=1

y=2x=2*1=2

(x,y)=(1,2)

C=2pir

=2*3.14*(1-2)'2

=6.28

Answer 2

Center at (3,6) and radius is 2 units.

Step-by-step explanation:

Given that x = 1 line is tangent to the circle at point (1,6).

So, y = 6 will be the equation of the radius line of the circle through the point (1,6).

{Since the tangent line and the radius line are perpendicular to each other}

Therefore, the intersection point of the lines y = 2x and y = 6 will be the center of the circle.

{Since the center of the circle lies on the line y = 2x}

Now, the solution point i.e. the intersection point of lines y = 2x and y = 6 is point (3,6).

Hence, the center of the circle is at point (3,6) and its radius is the distance between points (1,6) and (3,6) i.e. 2 units. (Answer)