The point of Intersection of Y=x Square -3x-4 And x- Axis are
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Step-by-step explanation:
Given lines are x+y=4 and x−y=2
On solving these lines, we get
x=3 and y=1
Now, the equation of line which passes through the intersection point (3,1) having slope
θ=tan
−1
(
4
3
) is (y−1)=
4
3
(x−3)
⇒ 4y−4=3x−9
⇒ 3x−4y=5.....(i)
Now for the intersection point of the line (i) with parabola y
2
=4(x−3). Put y=(
4
3x−5
), then we get
16
(3−5x)
2
=4(x−3)
⇒9x
2
+25−30x=54x−192
⇒9x
2
−94x+217=0
⇒x=
18
94±
8836−7812
=
18
94±
1024
⇒x=
18
94±32
=
8
126
or
18
62
⇒x
1
=
3
21
=7;x
2
=
9
31
∣x
1
−x
2
∣=
∣
∣
∣
∣
∣
∣
7−
9
31
∣
∣
∣
∣
∣
∣
=
∣
∣
∣
∣
∣
∣
9
32
∣
∣
∣
∣
∣
∣
=
9
32
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