JEE Mains · Maths · STD 11 - 9. straight line
Let a variable line of slope \(m>0\) passing through the point \((4,-9)\) intersect the coordinate axes at the points \(A\) and \(B\). the minimum value of the sum of the distances of \(\mathrm{A}\) and \(\mathrm{B}\) from the origin is
- A \(25\)
- B \(30\)
- C \(15\)
- D \(10\)
Answer & Solution
Correct Answer
(A) \(25\)
Step-by-step Solution
Detailed explanation
equation of line is \( y+9=m(x-4) \) \( \therefore \quad A=\left(\frac{9+4 m}{m}, 0\right) \) \( \quad B=(0,-9-4 m) \) \( \therefore \quad O A+O B=\frac{9+4 m}{m}+9+4 m\) \( \because \mathrm{m}>0 \) \( =13+\frac{9}{\mathrm{~m}}+4 \mathrm{~m} \)…
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