If x=a tan tita and y=b sec tita then

Answer 1

To find the relationship between x and y when x = a tan(tita) and y = b sec(tita), we can use trigonometric identities.

First, we can write tan(tita) = y/a and sec(tita) = b/y.

Now, we can use the identity sec(tita) = 1/cos(tita) to substitute for sec(tita) in terms of y:

sec(tita) = b/y
1/cos(tita) = b/y
cos(tita) = y/b

Next, we can write tan(tita) = sin(tita)/cos(tita) = y/a in terms of sin(tita):

sin(tita) = (y/a)cos(tita) = y/a * (y/b) = y^2 / (ab)

Therefore, the relationship between x and y is given by sin(tita) = y^2 / (ab).

Answer 2

clearly, "tita" is meant to mean θ. so, if
x = atanθ
y = bsecθ,
we have
tanθ = x/a
secθ = y/b
and then
sec^2θ = 1+tan^2θ
so
(y/b)^2 = 1 + (x/a)^2
y^2/b^2 - x^2/a^2 = 1

Answer 3

That is correct. The relationship between x and y can be expressed as:

y^2/b^2 - x^2/a^2 = 1

This equation represents a hyperbola in the xy-plane with center at the origin and transverse axis along the y-axis (parallel to the y-axis). The hyperbola will have vertices along the y-axis at (0, ±b) and asymptotes at y = ±(bx/a).