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10 cards from this deck
To define xxx and yyy as functions of a parameter ttt.
dy/dx=(dy/dt)/(dx/dt)dy/dx = (dy/dt) / (dx/dt)dy/dx=(dy/dt)/(dx/dt) using the chain rule.
d2ydx2=ddt(dydx)dxdt\frac{d^2y}{dx^2} = \frac{\frac{d}{dt}(\frac{dy}{dx})}{\frac{dx}{dt}}dx2d2yโ=dtdxโdtdโ(dxdyโ)โ.
Differentiate x=f(t)x = f(t)x=f(t) and y=g(t)y = g(t)y=g(t) with respect to ttt.
Use yโy1=m(xโx1)y - y_1 = m(x - x_1)yโy1โ=m(xโx1โ) with m=dy/dtdx/dtm = \frac{dy/dt}{dx/dt}m=dx/dtdy/dtโ.
Differentiate xxx and yyy, then divide dydydy by dxdxdx.
The point is (2,2)(\sqrt{2}, \sqrt{2})(2โ,2โ) when ฮธ=ฯ/4\theta = \pi/4ฮธ=ฯ/4 on the curve.
Solve tโ1=3(1/(t+1))t - 1 = 3(1/(t+1))tโ1=3(1/(t+1)).
y=2(x+1)โ1y = 2(x + 1) - 1y=2(x+1)โ1, normal point (โ1,โ1)(-1, -1)(โ1,โ1).
The Cartesian equation is y=1xโ2y = \frac{1}{x} - 2y=x1โโ2.
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