- #1

AnnaSuxCalc

- 55

- 0

**An Unknown Conic and Equation of Tangent Line **HELP****

## Homework Statement

(a) Find the positive y-coordinate of the point

__on__the conic whose x-coordinate is 27cos[tex]\theta[/tex], where 0<[tex]\theta[/tex]<[tex]\pi[/tex]/2

(b) The slope of the tangent line to the conic through the point (27cos[tex]\theta[/tex], y

_{1}) is -1/27cot[tex]\theta[/tex], where y

_{1}is your solution in part (a). Find the equation of the tangent line to the conic through the point (27cos[tex]\theta[/tex], y

_{1})

(c) Write an expression for

*S*where

*S*is the sum of the x- and y-intercepts of the tangent line that you computed in part (b)

(d) If [tex]\theta[/tex] = tan

^{-1}(1/3), show that the value of

*S*is 10

^{3/2}

## Homework Equations

x

^{2}/ 27

^{2}+ y

^{2}= 1

## The Attempt at a Solution

okay sooo...

because it has the + sign I think it is an Ellipse with the general equation of:

(x-h)

^{2}/a

^{2}

**+**(y-k)

^{2}/b

^{2}= 1

BUT I graphed it using my calculator and it gave me an almost straight line, to do this I rearranged the equation to give:

y = 1 - [tex]\sqrt{x^2/27^2}[/tex]

for part (d)[tex]\theta[/tex] = tan

^{-1}(1/3) then tan[tex]\theta[/tex] = 1/3

YA...I'm stuck

PLEASE HELP Guys