Question

The equation of the lines through the points (2, 3) and making an intercept of length 2 unit between the lines y + 2x = 3 and y + 2x = 5, are

• A. x + 3 = 0, 3x + 4y = 12
• B. y – 2 = 0, 4x – 3y = 6
• C. x – 2 = 0, 3x + 4y = 18
• D. None of the above

Answer 1

The correct option is C x – 2 = 0, 3x + 4y = 18

$\frac{x-2}{cos\theta }=\frac{x-3}{sin\theta }=ror(r+2)\therefore [rsin\theta +3]+2\left[\right(r+2)cos\theta +2]=5subtracting,weget2sin\theta +4cos\theta =2.......\left(i\right)\therefore 2cos\theta =1-sin\theta \Rightarrow 4(1-si{n}^2\theta )=(1-sin\theta {)}^2\Rightarrow sin\theta =1or-\frac{3}{5}\text{and hence from equation (i)}cos\theta =0,\frac{4}{5}\therefore tan\theta =\infty or-\frac{3}{4}\therefore x-2=0and3x+4y=18$