Question

A circle of 50 mm diameter rolls along a straight line without slipping. Draw the curve traced out by a point P on the circumference, for one complete revolution of the circle. Name the curve. Draw a tangent to the curve at a point on it 40 mm from the line

Answer 1

Answer:

Any line through P(α,β) is

cosθ

x−α

​  

=  

sinθ

y−β

​  

=r (say)

It meets the given curve where

(rcosθ+α)  

2

+2h(rcosθ+α)(rsinθ+β)+b(rsinθ+β)  

2

=1

r  

2

(acos  

2

θ+2hcosθsinθ+bsin  

2

θ)+r()+(aα  

2

+2hαβ+bβ  

2

−1)=0

Above is a quadratic in r and gives two values of r say  

r  

1

​  

 and r  

2

​  

 which represent PQ and PR

∴PQ.PR=r  

1

​  

.r  

2

​  

 

=  

acos  

2

θ+2hcosθsinθ+bsin  

2

θ

aα  

2

+2hαβ+bβ  

2

−1

​  

 

Above result will be independent of slop i.e. θ if a=b

and h=0∵cos  

2

θ+sin  

2

θ=1  

Hence the given equation of curve becomes a circle as  

a=b and h=0.

solution

Step-by-step explanation: