the curve y=3√x-2 and the line 3x-4y+3=0 intersect at the points P and Q. find the length of PQ
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Given, P=(
3
,0)
Equation of line AB is
cos60
∘
x−
3
=
sin60
∘
y−0
=r(say)
⇒x=
3
+
2
r
,y
2
r
3
Therefore, point (
3
+
2
r
,
2
r
3
) lies on y
2
=x+2
⇒
4
3r
2
=
3
+
2
r
+2
⇒
4
3r
2
−
2
r
−(2+
3
)=0
Let the roots be r
1
and r
2
, then the product
r
1
×r
2
=PA⋅PB=
∣
∣
∣
∣
∣
∣
∣
∣
4
3
−(2+
3
)
∣
∣
∣
∣
∣
∣
∣
∣
=
3
4(2+
3
)
.
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