Find the The Slopes of the tangent and the normal to the following curves at the indicated points :
x = a (θ – sin θ), y = a(1 + cos θ) at
θ = – π/2
Given:
x = a(
) & y = a(1 + cos
) at 
Here, To find 
, we have to find 
& 
and and divide 
and we get our desired 
.
(xn) = n.xn – 1
⇒ x = a(
)
⇒ 
= a(
(
) – 
(sin
))
⇒ 
= a(1 – 
) ...(1)
(sinx) = cosx
⇒ y = a(1 + cos
)
⇒ 
= a(
(
) + 
(cos
))
(cosx) = – sinx
(Constant) = 0
⇒ 
= a(
+ ( – sin
))
⇒ 
= a( – sin
)
⇒ 
= – asin
...(2)
⇒ 
⇒ 
The Slope of the tangent is 
Since, 
⇒ 
sin(
) = 1
cos(
) = 0
⇒ 
⇒ 
⇒ 
= 1
The Slope of the tangent at x = 
is 1
⇒ The Slope of the normal = 
⇒ The Slope of the normal = 
⇒ The Slope of the normal = 
⇒ The Slope of the normal = – 1
1