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Magazine Problem 1
The locus of a point in the plane that moves such that its distance from a fixed point (focus) is in a constant ratio to its distance from a fixed line (directrix) is a _____.
Problem 7
Find the slope of the line with inclination \(\theta\). $$\theta=\frac{3 \pi}{4} \text { radians }$$
Problem 10
(A) sketch the curve represented by the parametric equations (indicate the orientation of the curve) and (b) eliminate the parameter and write the resulting rectangular equation whose graph represents the curve. Adjust the domain of the rectangular equation, if necessary. $$\begin{aligned} &x=3-2 t\\\ &y=2+3 t \end{aligned}$$
Problem 11
Find the standard form of the equation of the ellipse with the given characteristics and center at the origin. Vertices: (卤7,0)\(;\) foci: (卤2,0)
Problem 14
Rotate the axes to eliminate the \(x y\) -term in the equation. Then write the equation in standard form. Sketch the graph of the resulting equation, showing both sets of axes. $$x y-4=0$$
Problem 14
(A) sketch the curve represented by the parametric equations (indicate the orientation of the curve) and (b) eliminate the parameter and write the resulting rectangular equation whose graph represents the curve. Adjust the domain of the rectangular equation, if necessary. $$\begin{aligned} &x=t-3\\\ &y=t^{2} \end{aligned}$$
Problem 19
(A) sketch the curve represented by the parametric equations (indicate the orientation of the curve) and (b) eliminate the parameter and write the resulting rectangular equation whose graph represents the curve. Adjust the domain of the rectangular equation, if necessary. $$\begin{aligned} &x=t+1\\\ &y=\frac{t}{t+1} \end{aligned}$$
Problem 25
Find the standard form of the equation of the parabola with the given characteristic(s) and vertex at the origin. Vertical axis and passes through the point (4,6)
Problem 33
A point in polar coordinates is given. Convert the point to rectangular coordinates. $$(-2.5,1.1)$$
Problem 39
(a) use the discriminant to classify the graph of the equation, (b) use the Quadratic Formula to solve for \(y\) and (c) use a graphing utility to graph the equation. $$12 x^{2}-6 x y+7 y^{2}-45=0$$
