Straight Lines
Grade None
Question:
<p>The x-intercept of angle bisector of angle between the lines 2x + y - 2 = 0 and 2x + 4y + 7 = 0 which contains the fixed point on the family of lines (2cos<span class="math-tex">\(\alpha\)</span> + 3 sin<span class="math-tex">\(\alpha\)</span>)x + (3 cos<span class="math-tex">\(\alpha\)</span> - 5 sin<span class="math-tex">\(\alpha\)</span>)y = 5 cos<span class="math-tex">\(\alpha\)</span> - 2 sin<span class="math-tex">\(\alpha\)</span> for different values of <span class="math-tex">\(\alpha\)</span>, is equal to :</p>
<p style="display:inline"><span class="math-tex">\(-\frac{11}{2}\)</span></p>
<p style="display:inline"><span class="math-tex">\(\frac{11}{2}\)</span></p>
<p style="display:inline"><span class="math-tex">\(\frac{1}{2}\)</span></p>
<p style="display:inline"><span class="math-tex">\(-\frac{1}{2}\)</span></p>
Step-by-Step Solution
Key Concept: Identify the fixed point of the family of lines and determine the specific angle bisector that contains this point by evaluating the signs of the line expressions at that point.
<p><span class="math-tex">\(\frac{11}{2}\)</span></p>
Correct Answer: B