The differential equation of all circles having their centres on the line y = 5 and touching the X-axis is
A. \(y^{2}\left(1+\frac{d y}{d x}\right)=25\)
B. \((y-5)^{2}\left[1+\left(\frac{d y}{d x}\right)^{2}\right]=25\)
C. \((y-5)^{2}+\left[1+\left(\frac{d y}{d x}\right)^{2}\right]=25\)
D. \((y-5)^{2}\left[1-\left(\frac{d y}{d x}\right)^{2}\right]=25\)
Answer:B
The differential equation of all circles having their centres on the line y = 5 and touching the X-axis is
A. \(y^{2}\left(1+\frac{d y}{d x}\right)=25\) B. \((y-5)^{2}\left[1+\left(\frac{d y}{d x}\right)^{2}\right]=25\) C. \((y-5)^{2}+\left[1+\left(\frac{d y}{d x}\right)^{2}\right]=25\) D. \((y-5)^{2}\left[1-\left(\frac{d y}{d x}\right)^{2}\right]=25\)