STATEMENT – 1 : If the circles $x^{2} + y^{2} + 2 g x + 2 f y = 0$ and $x^{2} + y^{2} + 2 g^{1} x + 2 f^{1} y = 0$ touch each other then $f^{1} g = f g^{1} .$
STATEMENT- 2: Let C be any circle with centre $(0, \sqrt{2}) .$ There can be atmost 2 points with rational coordinates on C.
STATEMENT- 3: Circle $x^{2} + y^{2} - 6 x - 4 y + 9 = 0$ bisects the circumference of the circle $x^{2} + y^{2} - 8 x - 6 y + 23 = 0$
STATEMENT- 4: If centre of first circle lie on the second circle then it bisects circumference of second circle
Which of the following must be truth value of above statements in that order

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answer is D.

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Detailed Solution

Use the conept $C_{1} C_{2} = r_{1} + r_{2}$

If the radical axis is passing through the centre of first circle , then second circle bisects the circumfernec of first circle

Statement 4 is false

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