Question

The equation of the circle with centre on x-axis, radius 5 and passing through the point (2, 3), is.

• A. $x ^ { 2 } + y ^ { 2 } + 4 x - 21 = 0$
• B. $x ^ { 2 } + y ^ { 2 } + 4 x + 21 = 0$
• C. $x ^ { 2 } + y ^ { 2 } - 4 x - 21 = 0$
• D. $x ^ { 2 } + y ^ { 2 } + 5 x - 21 = 0$

Answer 1

Answer: (A)

$x ^ { 2 } + y ^ { 2 } + 4 x - 21 = 0$

Answer 2

Let centre be $( - g , 0 )$, then $\sqrt { g ^ { 2 } - c } = 5 \Rightarrow c = g ^ { 2 } - 25$

Also it passes through (2, 3), therefore

$13 + 4 g + g ^ { 2 } - 25 = 0 \Rightarrow g = - 6,2$

Hence the equations are $x ^ { 2 } + y ^ { 2 } - 12 x + 11 = 0$ and

$x ^ { 2 } + y ^ { 2 } + 4 x - 21 = 0$.