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NIMCET 2015 — Mathematics PYQ

NIMCET | Mathematics | 2015

If two circles $x^2 + y^2 + 2gx + 2fy = 0$ and $x^2 + y^2 + 2g'x + 2f'y = 0$ touch each other, then which of the following is true?

Choose the correct answer:

Explanation

1. Centers of Circles:

Center $C_1 = (-g, -f)$

Center $C_2 = (-g', -f')$

Point of contact = $(0,0)$ (Origin)

2. Collinearity Condition:

Since both circles touch at the origin, the centers and the origin are collinear.

\text{Slope of } OC_1 = \text{Slope of } OC_2

\frac{-f}{-g} = \frac{-f'}{-g'}

\frac{f}{g} = \frac{f'}{g'}

3. Final Solving:

f g' = f' g

g'f = gf'

Conclusion:

Correct option is (b).