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 from This Point.

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Question

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 from this point.

diffcult

Solution

Correct option is

15^o, 75^o

Let the straight line makes an angle θ with the positive direction of x-axis.

∴ Equation of the line through (1, 2) in parametric form is

Since the point lies on the line

x + y = 4

for n = 0,

= 15^o, 75^o.

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