91Ó°ÊÓ

Find the distance between the point and the line. $$\begin{array}{cc}\text{Point} && \text{Line} \\ (6,2) && -3 x+4 y=-5\end{array}$$

Find a set of parametric equations to represent the graph of the rectangular equation using (a) \(t=x\) and \((b) t=2-x\) $$y=3 x^{2}+1$$

Use a graphing utility to find one set of polar coordinates of the point given in rectangular coordinates. $$\left(\frac{7}{4}, \frac{3}{2}\right)$$

Find a set of parametric equations to represent the graph of the rectangular equation using (a) \(t=x\) and \((b) t=2-x\) $$y=6 x^{2}-5$$

Find the distance between the point and the line. $$\begin{array}{cc}\text{Point} && \text{Line} \\ (1,-3) && 4 x-3 y=-7\end{array}$$

Use a graphing utility to find one set of polar coordinates of the point given in rectangular coordinates. $$\left(-\frac{7}{9},-\frac{3}{4}\right)$$

Determine whether the statement is true or false. Justify your answer. The graph of \(r=10 \sin 5 \theta\) is a rose curve with five petals.

Find a set of parametric equations to represent the graph of the rectangular equation using (a) \(t=x\) and \((b) t=2-x\) $$y=1-2 x^{2}$$

Show that \(a^{2}=b^{2}+c^{2}\) for the ellipse $$\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1$$ where \(a \geq 0, b>0,\) and the distance from the center of the ellipse (0,0) to a focus is \(c .\)

Find the distance between the point and the line. $$\begin{array}{cc}\text{Point} && \text{Line} \\ (-1,2) && 5 x+3 y=-4\end{array}$$