If the line x-1/2=y-2/3=t intersects the line x + y = 8 , then t is
a) 1
b) 2.
c)3
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Answered by
1
Answer:
Given equation of line is
y=x−1
Given equation of parabola is
y
2
=4x
⇒(x−1)
2
=4x
⇒x
2
−6x+1=0
⇒x=3±
8
∴y=2±
8
So, the line intersects the parabola at points A(3+
8
,2+
8
) and B(3−
8
,2−
8
)
Suppose point D is (x
3
,y
3
), then the sum of ordinates of the feets of normals drawn from point C is 0.
y
1
+y
2
+y
3
=0
⇒2+
8
+2−
8
+y
3
=0
⇒y
3
=−4
⇒x
3
=4
Therefore, the point is (4,−4).
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