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 63 from the given point ' A '. Find the angle which the line mak…

Question

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 63 from the given point ' A '. Find the angle which the line makes with the positive direction of X-axis.

Accepted Answer

Correct answer: A. (a) Let be the angle which the line makes with positive direction of x-axis and this line passes through point A (1 ,2 ), so equation of line is x-1 cos ⁡ = y-2 sin ⁡ = 63 ∴ General point on the line is P(1 63 cos ⁡ ,2 63 sin ⁡ ) Let this point P is on the straight line x+y=4, so 1 63 cos ⁡ +2 63 sin ⁡ =4 ⇒ 63 ( sin ⁡ + cos ⁡ )=1 On squaring both sides, we get 69( sin^2 ⁡ + cos^2 ⁡ +2 sin ⁡ cos ⁡ )=1 ⇒1+ sin ⁡2 = 32 sin ⁡2 = 12 ⇒2 =30^ and150^ ⇒ =15^ and75^

$A straight line is drawn through the point A (1, 2) such that its point of intersection with the straight line x + y = 4 is at a distance \frac{6}{3} from the given point ' A'. Find the angle which the line makes with the positive direction of X -axis.$

Solution

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