a line passes through p ( 3,2) . if it meets the x axis at a and y axis at b . If PA /PB = 2/3 . find the equation of the line passing through 3,2 and perpendicular to AB
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Answer:
Given,
a line x+2y−7=0
and point P=(1,2)
angle θ=45
o
here, equation of line through point
′
P
′
na dangle 45
o
with x−axis is
(y−y
1
)=m(x−x
1
)x
1
y
1
(1,2)
m=tan45
o
m=1
⇒ (y−2)=1(x−1)⟺ y−2=x−1
⇒ y=x−1+2
⇒ y=x+1
Let us substitute
′
y
′
value in x+2y−7=0
x+2(x+1)−7=0
⇒ x+2x+2−7=0
⇒ 3x−5=0⟺x=5/3
Substitute
′
x
′
in y=x+1
⇒ y=
3
5
+1⟺ y=
3
8
∴ the line x+2y−7=0
meets at point (5/3,/3)
the distance of PQis
PQ=
(x
2
−x
1
)
2
+(y
2
−y
1
2
)
PQ=
(
3
5
−1)
2
+(
3
8
−2)
2
⇒
(
3
2
)
2
+(
3
2
)
2
⇒
9
4
+
9
4
PQ=
9
8
=
3
2
2
∴ PQ=
3
2
2
∵
8
=2
2
9
=3
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