Question

Let a line y = mx(m > 0) intersects the parabola y2
= x at a point P, other than the origin. Let the tangent to it
at P meet the x-axis at the point Q. If area ( OPQ ) = 4 sq. units, then m is equal to

Answer 1

Answer:

Let P≡(t  

2

,t)

tangent at P

2ty=x+t  

2

 

for Q       y=0

x=−t  

2

 

∴Q≡(−t  

2

,0)

y  

2

=x

⇒m  

2

x  

2

=x

⇒x=  

m  

2

 

1

​  

 

⇒t  

2

=  

m  

2

 

1

​  

⇒∣t∣=  

∣m∣

1

​  

 

from Question

2

1

​  

 

∣

∣

∣

∣

∣

∣

∣

∣

​  

 

0

t  

2

 

−t  

2

 

​  

 

0

t

0

​  

 

1

1

1

​  

 

∣

∣

∣

∣

∣

∣

∣

∣

​  

=4

⇒∣t  

3

∣=8

⇒t=±2

⇒m=±  

2

1

​  

 

∴m=  

2

1

[since m>0]

Step-by-step explanation:

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Answer 2

Answer:

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Step-by-step explanation:

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