9. x=asec θ, y = b tan θ
It is given that x and y are parametrically connected by the equations,
x = a sec θ (1)
And,
y = b tan θ (2)
Differentiate equation (2) with respect to θ .
d y d θ = b sec 2 θ
Differentiate equation (1) with respect to θ .
d x d θ = a ( sec θ tan θ )
We know that,
d y d x = d y d θ d x d θ
Substitute the value of d y d θ and d x d θ .
d y d x = b sec 2 θ a sec θ tan θ d y d x = b sec θ a tan θ d y d x = b × 1 cos θ × cos θ a sin θ d y d x = b a cos e c θ
Thus, the solution is d y d x = b a cos e c θ .
It is given that
And,
Differentiate equation (2) with respect to
Differentiate equation (1) with respect to
We know that,
Substitute the value of
Thus, the solution is
