COMEDK · Maths · 10. Straight Lines
Find the direction in which a straight line must be drawn through the point \((1,2)\) so that its point of intersection with the line \(x+y=4\) may be at a distance of \(\sqrt{\dfrac{2}{3}}\) from this point.
- A \(30^{\circ} \text { or } 150^{\circ}\)
- B \(15^{\circ} \text { or } 75^{\circ}\)
- C \(60^{\circ} \text { or } 120^{\circ}\)
- D \(50^{\circ} \text { or } 100^{\circ}\)
Answer & Solution
Correct Answer
(B) \(15^{\circ} \text { or } 75^{\circ}\)
Step-by-step Solution
Detailed explanation
Let the line pass through the point \(P(1, 2)\) at an angle \(\theta\) with the positive \(x\)-axis. The equation of the line in parametric form is \(\dfrac{x-1}{\cos \theta} = \dfrac{y-2}{\sin \theta} = r\), where \(r\) is the distance from \(P\). Any point on this line is…
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