Maths · Straight line: Various forms of equations of a line, intersection of lines, angles between two lines
Line passes through point (1,2) and intersects the positive and axes at \) and \
Line \( A B \) passes through point (1,2) and intersects the positive \( x \) and \( y \) axes at \( \boldsymbol{A}(\boldsymbol{a}, \boldsymbol{0}) \) and \( \boldsymbol{B}(\boldsymbol{0}, \boldsymbol{b}) \) respectively. If the area of \( \triangle A O B \) is 1 unit the value of \( (2 a-b)^{2} \) is
- A. 220
- B. 240
- C. 248
- D. 284
Step-by-step solution
The line in intercept form is x/a + y/b = 1. It passes through (1,2) giving 1/a + 2/b = 1. The area of triangle AOB is (1/2)ab = 1, so ab = 2. Solving yields a^2 - a + 1 = 0, which has no real solution, indicating a possible misprint. Assuming the intended area is 10 (since it yields real intercepts and matches an option), then (1/2)ab = 10 gives ab = 20. Together with 1/a + 2/b = 1, we get 2a + b = 20. Solving gives a = 5 ± √15, b = 10 ∓ 2√15. Then (2a - b)^2 = (±4√15)^2 = 240.
Related MCQs
- Tow consecutive sides of a parallelogram are and If the equation to one diagonal is , then the equation of the other diagonal is…
- Solve graphically, the following pairs of equations:…
- If \) is the point lying on the graph of the equation then find…
- Classify the following pair of line as coincident, parallel or intersecting \&…
- If the points with position vectors and are collinear then…