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

see full answer

Talk to JEE/NEET 2025 Toppers - Learn What Actually Works!

Real Strategies. Real People. Real Success Stories - Just 1 call away

An Intiative by Sri Chaitanya

TTTT

FTTF

TFTF

TTTF

answer is D.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

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

Watch 3-min video & get full concept clarity

JEE

NEET

Foundation JEE

Foundation NEET

CBSE