Question

The tangent to the curve $x=1/t,y=t$ $-1/t$ at $t=2$ has _____ x-intercept and _____ y-intercept.

• A. $positive,positive$
• B. $positive,negative$
• C. $negative,positive$
• D. $negative,negative$

Answer 1

The correct option is A $positive,positive$

$x=\frac{1}{t};y=t-\frac{1}{t}$

$\frac{dy}{dx}{\mid }_{t=2}=\frac{dy/dt}{dx/dt}=\frac{1+\frac{1}{t^2}}{-\frac{1}{t^2}}=\frac{t^2+1}{-1}$

$\frac{dy}{dx}{|}_{t=2}=\frac{2^2+1}{-1}=-5$

$m_{tangent}=-5$

$x=\frac{1}{2},y=2-\frac{1}{2}=\frac{3}{2}$

equation of tangent $\Rightarrow$

$y-\frac{3}{2}=-5(x-\frac{1}{2})$

$\Rightarrow 2y+10x-3-5=0$

$5x+y=4$

x- Intercept = 4/5 $\}$ positive

y- Intercept = 4