Question

find the slope of normal to the curve x=a sec theta, y=atan theta at theta =π/6​

Answer 1

Answer:

if y=7x+1/x then find dy/dc

Answer 2

Given,

x = a secθ

y = a tanθ

To find,

The slope of the normal to the curve at θ = $\frac{\pi }{6}$

Solution,

The slope of the normal to the curve at θ = $\frac{\pi }{6}$ is $-\frac{1}{2}$.

We can simply solve the mathematical problem by the following procedure.

It is given that,

x = a secθ

y = a tanθ

We know that,

The slope of the tangent to the curve = $\frac{dy}{dx}$

Thus,

The slope of the tangent to the curve = $\frac{dy}{do} * \frac{do}{dx}$

                                                               = $\frac{a*sec^2o}{a*seco* tano}$

                                                               = cosec θ

Now,

We know that;

The slope of the normal is equal to the negative reciprocal of the slope of the tangent.

Thus,

The slope of the normal to the curve = - sinθ

On substituting the value of theta;

The slope of the normal to the curve = - sin (30)

                                                              = $-\frac{1}{2}$

Thus,

The slope of the normal to the curve at θ = $\frac{\pi }{6}$ is $-\frac{1}{2}$.