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BITSAT 2024
Exam
BITSAT
Year
2024
Subject
Mathematics
Chapter
Area Under Curves

BITSAT 2024 · Mathematics · Area Under Curves

If a, c, b are in GP, then the area of the triangle formed by the...

If a,c,ba, c, b are in GP, then the area of the triangle formed by the lines ax+by+c=0a x+b y+c=0 with the coordinates axes is equal to

Options

  1. A1
  2. B2
  3. C12\frac{1}{2}
  4. DNone of these

Correct answer

C. 12\frac{1}{2}

Step-by-step solution

Given a,c,ba, c, b are in GP ⇒c2=ab\Rightarrow \quad c^2=a b...(i) According to question, ∴ Area of △OAB=∣12×OA×OB∣=∣12×(−cb)×(−ca)∣=12×c2ab=12[byEq.(i)]\begin{aligned} \therefore \text{ Area of } \triangle O A B & =\left|\frac{1}{2} \times O A \times O B\right| \\ = & \left|\frac{1}{2} \times\left(\frac{-c}{b}\right) \times\left(\frac{-c}{a}\right)\right| \\ & =\frac{1}{2} \times \frac{c^2}{a b}=\frac{1}{2} [by Eq. (i)] \end{aligned}
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