AP EAMCET · Maths · Straight Lines
A straight line is drawn through the point \(A(1,2)\) such that its point of intersection with the straight line \(x+y=4\) is at a distance \(\frac{\sqrt{6}}{3}\)
from the given point ' \(A\) '. Find the angle which the line makes with the positive direction of \(X\)-axis.
- A \(\theta=15^{\circ}\) and \(75^{\circ}\)
- B \(\theta=75^{\circ}\) and \(45^{\circ}\)
- C \(\theta=45^{\circ}\) and \(60^{\circ}\)
- D \(\theta=60^{\circ}\) and \(30^{\circ}\)
Answer & Solution
Correct Answer
(A) \(\theta=15^{\circ}\) and \(75^{\circ}\)
Step-by-step Solution
Detailed explanation
Let the angle of inclination of line \(\theta\), and as passed through point \(A(1,2)\), so equation of line is \(\frac{x-1}{\cos \theta}=\frac{y-2}{\sin \theta}= \pm \frac{\sqrt{6}}{3}\) \(\therefore\) General point on the line is…
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