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Question: Through the point (1, 2), a straight line is drawn so that its point of intersection with the line x...

Through the point (1, 2), a straight line is drawn so that its point of intersection with the line x + y = 4 is at a distance 63\frac { \sqrt { 6 } } { 3 }. The direction in which this line is drawn is –

A

300

B

450

C

600

D

750

Answer

750

Explanation

Solution

x + y = 4 ––– (2**)**

\ Point Q lies on the line (1), which is at 63\frac { \sqrt { 6 } } { 3 }

unit distances from the point P, \ r = 63\frac { \sqrt { 6 } } { 3 }

So,

Q point Q lies on the line (2)

Ž 1 + 63\frac { \sqrt { 6 } } { 3 }cos q + 2 + 63\frac { \sqrt { 6 } } { 3 } sin q = 4

Ž 63\frac { \sqrt { 6 } } { 3 } (sin q + cos q) = 1

Ž (sin q + cos q) = 32\sqrt { \frac { 3 } { 2 } }Ž q = 150 or 750