Question

If the straight line through the point (3,4)
makes an angle 30 with x-axis and meets
the line
12x + 5y +10=0 at Q find the length PQ
(Ans: 25/16 Sq. un​)
please give detailed answer

Answer 1

Answer:

Any line through P(3,4) making an angle

6

π

with x−axis is

cos30

o

x−3

=

sin30

o

y−4

=r

Where r represents the distance of any point on this line from the given point P(3,4)

Any point Q on it is (r

3

/2)+3,(r/2)+4 and Q lies on 12x+5y+10=0

∴12[(

2

r√3

)+3]+5(

2

r

+4)+10=0

∴(12

3

+5)r+132=0

∴r=

12√(3)+5

∣−132∣

=

12√(3)+5

132

.

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