Question

If the circle formed by the carabao's footprints is given by the equation x²+y²-6x+8y-119=0, how long is the carabao's rope if the scale is 1 meter is to 2 units? ​

Answer 1

Given circle:

$x^{2}+y^{2}-6x+8y-119=0$

To find:

The length of the rope if the scale is 1 meter is to 2 units

Step-by-step explanation:

The given circle is

$\quad x^{2}+y^{2}-6x+8y-129=0$

$\Rightarrow (x-3)^{2}+(y+4)^{2}=129+9+25$

$\Rightarrow (x-3)^{2}+(y+4)^{2}=144=12^{2}$

Thus the radius of the circle is $12\:units$, i.e., $6\:m$ since 1 m = 2 units.

To find the length of the rope, we find the perimeter of the circle of radius 6 m.

Thus the perimeter of the circle is

• $=2\pi\times 6\:m$
• $=12\pi\:m$
• $=37.68\:m$ where $\pi=3.14$

Answer:

$\therefore$ the length of the rope is 37.68 m