If the circles x 2 + y 2 = a 2 and x 2 + y 2 − 2 gx + g 2 − b 2 = 0 touch each other externally, then

Open MARKS Web Download App

Search any question & find its solution

Question: Answered & Verified by Expert

If the circles $x^2+y^2=a^2$ and $x^2+y^2-2 g x+g^2-b^2=0$ touch each other externally, then

MathematicsCircleJEE Main

Options:

A $g=a b$
B $g^2=a^2+b^2$
C $g^2=a b$
D $g=a+b$

Solution:

1749 Upvotes Verified Answer

The correct answer is: $g=a+b$

According to the condition, $\sqrt{(g-0)^2+(0-0)^2}=a+b \Rightarrow g=a+b$

Looking for more such questions to practice?

Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.

Use on iOS or Desktop Download from Google Play