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TS EAMCET · Maths · Straight Lines

A straight line which makes equal intercepts on positive \(X\) and \(Y\) axes and which is at a distance 1 unit from the origin intersects the straight line \(y=2 x+3+\sqrt{2}\) at \(\left(x_0, y_0\right)\). Then \(2 x_0+y_0\) is equal to

  1. A \(3+\sqrt{2}\)
  2. B \(\sqrt{2}-1\)
  3. C 1
  4. D 0
Verified Solution

Answer & Solution

Correct Answer

(B) \(\sqrt{2}-1\)

Step-by-step Solution

Detailed explanation

The equation of line \(A B\) which makes an equal intercepts on positive \(x\) and \(y\) axes are \(\frac{x}{a}+\frac{y}{a}=1\) ie, \(\quad x+y=a\) ...(i) Distance of Eq. (i) from origin \(=1\) \(\left|\frac{0+0-a}{\sqrt{1+1}}\right|=1, \frac{-a}{\sqrt{2}} \mid=1\)…