Question

a circle C2 has the equation x2 y2 -8x 12y k = 0 given than c2 likes entirely in the fourth quadrant, find the range of values of k

Answer 1

Hi,

`\boxed{36\leq k\leq 52}`

Explanation:

Equation of the circle:

`x^2+y^2-8x+12y+k=0\\x^2-2*4*x+16+y^2+2*6*y+36+k-16-36=0\\(x-4)^2+(y+6)^2=52-k\\\\Center=(4,-6)\\min(|4|,|-6|)=4\\\\The\ circle\ is\ entirely\ in\ the\ 4th\ quadrant\ if\\\\4\geq √(52-k) \geq 0\\\\0\leq 52-k\leq 16\\\\0\geq -52+k\geq -16\\\\52\geq k\geq 36\\\\\\`