Straight Line Question 102

Question: If $ 2p $ is the length of perpendicular from the origin to the lines $ \frac{x}{a}+\frac{y}{b}=1 $ , then $ a^{2},8p^{2},b^{2} $ are in

Options:

A)A. P.

B)G.P.

C)H. P.

D)None of these

Show Answer

Answer:

Correct Answer: C

Solution:

  • We have $ 2p=| \frac{0+0-1}{\sqrt{\frac{1}{a^{2}}+\frac{1}{b^{2}}}} |\Rightarrow \frac{1}{a^{2}}+\frac{1}{b^{2}}=\frac{1}{4p^{2}} $
    Þ $ \frac{1}{a^{2}}+\frac{1}{b^{2}}=\frac{2}{8p^{2}}\Rightarrow \frac{1}{a^{2}},\frac{1}{8p^{2}},\frac{1}{b^{2}} $ are in A. P.
    Þ $ a^{2},8p^{2},p^{2} $ are in H.P .