Q77 / 125 · BITSAT 2020 · Mathematics

If $a, c, b$ are in G.P., then the area of the triangle formed by the lines $a x+b y+c=0$ with the coordinates axes is equal to

  • A
    1
  • B
    2
  • Correct answer
    C
    $\frac{1}{2}$
  • D
    None of these

Solution

Area of the triangle $=\frac{1}{2}(\mathrm{x}$ intercept $) \times(\mathrm{y}$ intercept $)$ $=\frac{1}{2}\left(-\frac{\mathrm{c}}{\mathrm{a}}\right)\left(-\frac{\mathrm{c}}{\mathrm{b}}\right)=\frac{1}{2} \frac{\mathrm{c}^{2}}{\mathrm{ab}}=\frac{1}{2} \mathrm{unit}$ $\left[\because \mathrm{a}, \mathrm{c}, \mathrm{b}\right.$ are in $\left.\mathrm{G} . \mathrm{P} . \Rightarrow \mathrm{c}^{2}=\mathrm{ab}\right]$

Hence, the correct answer is option: 'C'.

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