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TS EAMCET · Maths · Straight Lines

If the perpendicular drawn from the point \((2,-3)\) to the straight line \(4 x-3 y+8=0\) meets it at \(\mathrm{M}(a, b)\) and \(a^3-b^3=\mathrm{k}^3\), then \(\mathrm{k}=\)

  1. A 1
  2. B -1
  3. C 2
  4. D -2
Verified Solution

Answer & Solution

Correct Answer

(D) -2

Step-by-step Solution

Detailed explanation

\(m_{line} = \frac{4}{3}\) \(m_{\perp} = -\frac{3}{4}\) Equation of perpendicular: \(y - (-3) = -\frac{3}{4}(x - 2) \implies 3x + 4y + 6 = 0\) System of equations: \(4x - 3y + 8 = 0\) \(3x + 4y + 6 = 0\) Multiply first by 4, second by 3: \(16x - 12y + 32 = 0\)…