Straight Lines
General
Grade 11
Question:
The area of the parallelogram formed by the lines <span class="math-inline">3x + 4y = 7a</span>; <span class="math-inline">3x + 4y = 7b</span>; <span class="math-inline">4x + 3y = 7c</span> and <span class="math-inline">4x + 3y = 7d</span> is-
<span class="math-inline">\(\frac{|a-b|(c-d)|}{7}\)</span>
<span class="math-inline">|a - b| (c - d)|</span>
<span class="math-inline">\(\frac{|a-b|(c-d)|}{49}\)</span>
<span class="math-inline">7|a - b| (c - d)|</span>
Step-by-Step Solution
Key Concept: General
Since (1, 4) lies inside the circle <br> S1 < 0 <br> (1)² + (4)² - 6(1) - 10(4) + k < 0 <br> k < 29 <br> Also centre of given circle is (3, 5) and circle does not touch or intersect the coordinate axes <br> r < CA & r < CB <br> CA = 5 <br> CB = 3 <br> r < 5 & r < 3 <br> r < 3 or r² < 9 <br> r² = 9 + 25 - k <br> r² = 34 - k ⇒ 34 - k < 9 <br> k < 25 <br> k ∈ (25, 29)
Correct Answer: k < 29, k > 25