TS EAMCET · Maths · Straight Lines
If a line \(a x+2 y=k\) forms a triangle of area 3 sq. units with the coordinate axis and is perpendicular to the line \(2 x-3 y+7=0\), then the product of all the possible values of \(\mathrm{k}\) is
- A \(-36\)
- B \(36\)
- C \(-64\)
- D \(64\)
Answer & Solution
Correct Answer
(A) \(-36\)
Step-by-step Solution
Detailed explanation
\(a x+2 y=k\) is perpendicular to \(2 x-3 y+7=0\) \[ \begin{aligned} & \therefore m_1 \cdot m_2=-1 \\ & \frac{-a}{2} \times \frac{2}{3}=-1 \Rightarrow a=3 \end{aligned} \] \(\therefore 3 x+2 y=k\) forms triangle of area 3 sq. units \[ 3 x+2 y=k \]…
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