Question

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

• A. $x ^ { 2 } + y ^ { 2 } - 6 x - 5 y + 9 = 0$
• B. $x ^ { 2 } + y ^ { 2 } + 6 x + 5 y - 9 = 0$
• C. $x ^ { 2 } + y ^ { 2 } - 6 x + 5 y - 9 = 0$
• D. $x ^ { 2 } + y ^ { 2 } + 6 x - 5 y + 9 = 0$

Answer 1

Answer: (A)

$x ^ { 2 } + y ^ { 2 } - 6 x - 5 y + 9 = 0$

Answer 2

$k ^ { 2 } = 4 + ( k - 4 ) ^ { 2 } \Rightarrow k = \frac { 5 } { 2 }$

Hence required equation of circle is

$( x - 3 ) ^ { 2 } + \left( y - \frac { 5 } { 2 } \right) ^ { 2 } = \left( \frac { 5 } { 2 } \right) ^ { 2 } \Rightarrow x ^ { 2 } + y ^ { 2 } - 6 x - 5 y + 9 = 0$

Trick : Only (1) passes through (1, 4).