Conic Sections Question 245

Question: The line $ y=mx+c $ touches the curve $ \frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1 $ , if

[Kerala (Engg.) 2002]

Options:

A) $ c^{2}=a^{2}m^{2}+b^{2} $

B) $ c^{2}=a^{2}m^{2}-b^{2} $

C) $ c^{2}=b^{2}m^{2}-a^{2} $

D) $ a^{2}=b^{2}m^{2}+c^{2} $

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Answer:

Correct Answer: B

Solution:

$ y=mx+c $ touches the curve $ \frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1 $ , if $ c^{2}=a^{2}m^{2}-b^{2}. $