91Ó°ÊÓ

Find the rectangular coordinates for each of the points for which the polar coordinates are given. (8.0,-8.0)

Identify the curve represented by each of the given equations. Determine the appropriate important quantities for the curve and sketch the graph. $$4 x^{2}+4=9-8 x-4 y^{2}$$

Determine the center and radius of each circle.Sketch each circle. $$4(x+7)^{2}+4(y+11)^{2}=169$$

Find the inclinations of the lines with the given slopes. $$1.903$$

Determine whether the lines through the two pairs of points are parallel or perpendicular. $$(-1,-4) \text { and }(2,3) ;(-5,2) \text { and }(-19,8)$$

Solve the given problems. Find the equation of the hyperbola with vertices (-2,4) and \((-2,-2),\) and a conjugate axis of \(4,\) by use of the definition. Sketch the curve.

Solve the given problems. The equation of a hyperbola with center \((h, k)\) and transverse axis parallel to the \(x\) -axis is \(\frac{(x-h)^{2}}{a^{2}}-\frac{(y-k)^{2}}{b^{2}}=1 .\) (This is shown in Section \(21.7 .\) ) Sketch the hyperbola that has a transverse axis of \(4,\) a conjugate axis of \(6,\) and for which \((h, k)\) is (-3,2).

Find the polar equation of each of the given rectangular equations. \(x^{3}+y^{3}-4 x y=0\)

Solve the given problems. Show some applications of straight lines. Find the slope of the line joining points on the graph of \(y=x^{2}\) that have \(x\) -coordinates of \(-a\) and \(b(a>0, b>0)\)

Solve the given problems. The vertex and focus of one parabola are, respectively, the focus and vertex of a second parabola. Find the equation of the first parabola, if \(y^{2}=4 x\) is the equation of the second.