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AP EAMCET · Maths · Straight Lines

The midpoint of the diagonal of a rectangle formed by \(x^2+5 x-6=0\) and \(y^2-8 y-20=0\) is

  1. A \(\left(\frac{5}{2}, 4\right)\)
  2. B \(\left(\frac{-5}{2},-6\right)\)
  3. C \(\left(\frac{-5}{2}, 4\right)\)
  4. D \(\left(\frac{5}{2},-6\right)\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(\left(\frac{-5}{2}, 4\right)\)

Step-by-step Solution

Detailed explanation

\begin{aligned} & \text { } \mathrm{x}^2+5 \mathrm{x}-6=0 \Rightarrow \mathrm{x}^2+6 \mathrm{x}-\mathrm{x}-6=0 \\ & \Rightarrow(\mathrm{x}-1)(\mathrm{x}+6)=0 \Rightarrow \mathrm{x}_1, \mathrm{x}_2=1,-6 \\ & \mathrm{y}^2-8 \mathrm{y}-20=0 \Rightarrow \mathrm{y}^2-10 \mathrm{y}+2…