Question

EXAMPLE 1. The equation of the circle which touches
X-axis at (3, 0) and passes through (1, 4) is given by
2​

Answer 1

Answer:

Let the eq of circle be

x2+y2+2gx+2βy+c=0

now, x intercept = 2g2−c

But circle touches x axis ∴ x intercept = 0

∴2g2−c=0∴g2=c

∴eqn become x2+y2+3gx+2βy+g2=0

Now circle passes through (3, 0) and (1, 4) 

∴(3)2+(0)2+2g(3)+0+g2=0

9+6g+g2=0

∴g=−3

Also (1)2+(4)2+2(−3)(1)+2β(4)+9=0

∴1+16−6+8β+9=0

∴20+8β=0 ∴β=25

Hence eqn of circle is 

x