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Find a degree 
Magazine Problem 8
Graph the curve defined by the parametric equations. $$x=t, y=\sqrt{t^{2}+1}, t \text { in }[0,10]$$
Problem 8
The coordinates of a point in the \(x y\) -coordinate system are given. Assuming that the \(X Y\) -axes are found by rotating the \(x y\) -axes by the given angle \(\theta\), find the corresponding coordinates for the point in the \(X Y\) -system. $$(-2,0), \theta=30^{\circ}$$
Problem 8
Graph each ellipse. Label the center and vertices. $$\frac{x^{2}}{25}+\frac{y^{2}}{144}=1$$
Problem 8
Identify the conic section as a parabola, ellipse, circle, or hyperbola. $$4 x^{2}+8 y^{2}=30$$
Problem 8
Find the polar equation that represents the conic described (assume that a focus is at the origin). Conic Ellipse Eccentricity \(e=\frac{2}{3}\) Directrix \(x=-4\)
Problem 9
(a) identify the type of conic from the discriminant, (b) transform the equation in \(x\) and \(y\) into an equation in \(x\) and \(Y\) (without an \(X Y\) -term) by rotating the \(x\) - and \(y\) -axes by the indicated angle \(\theta\) to arrive at the new \(X\) - and \(Y\) -axes, and (c) graph the resulting equation (showing both sets of axes). $$x y-1=0, \theta=45^{\circ}$$
Problem 9
Identify the conic section as a parabola, ellipse, circle, or hyperbola. $$x^{2}-y=1$$
Problem 9
Graph each ellipse. Label the center and vertices. $$\frac{x^{2}}{100}+y^{2}=1$$
Problem 9
Find an equation for the parabola described. Vertex at (0,0)\(;\) focus at (0,3)
Problem 9
Find the polar equation that represents the conic described (assume that a focus is at the origin). Conic Hyperbola Eccentricity \(e=\frac{4}{3}\) Directrix \(x=-3\)
