Exam 22: Analytic Geometry

Write the equation of the ellipse, whose center is at the origin, and passes through $(-6,4)$ and $(8,3)$ , in general form.

Write the equation of the hyperbola in standard form: foci at $(-3,1)$ and $(5,1)$ , slope of asymptotes $= \pm 5 / 4$

Find the distance between the points $(8,5)$ and $(-7,-4)$ . Keep three significant digits.

Write the equation of the circle $x^{2}+y^{2}-4 x-10 y+20=0$ in standard form.

Write the equation, in general form, of the line: passes through $(5,-1)$ and is parallel to $2 x-3 y=8$

Write the equation of the ellipse centered is at the origin, with horizontal major axis 8 units long and a focus at $(1.5,0)$ .

Find the point(s) of intersection: $x^{2}+y^{2}-4 x+2 y-4=0$ and $x^{2}+y^{2}+2 x-4 y-11=0$

Write the equation, in general form, of the line: $y$ -intercept $=-1$ and perpendicular to $5 y-3 x=13$

Find the directed distance $A B: A(3.08,-2.37), B(-1.08,-2.37)$

Solve simultaneously to find the points of intersection (if any) of the ellipse with the given curve: $4 x^{2}+$ $9 y^{2}=36$ with $2 x+y-10=0$

How long does a ramp need to be in order to meet the requirements of not to exceed a slope of 0.08 , if its height is $30 \mathrm{~cm}$ .

Write the equation, in slope-intercept form, of the following line: $x$ -intercept $=-2 ; y$ -intercept $=4$ .

Write the equation in standard form of the ellipse $25 x^{2}+9 y^{2}-72 y-81=0$ .

Find the coordinates of vertices and foci for the ellipse: $\frac{x^{2}}{81}+\frac{y^{2}}{25}=1$

Under what condition (for $a$ and $b$ ), the asymptotes of the hyperbola $b^{2} x^{2}-a^{2} y^{2}=a^{2} b^{2}$ , will be perpendicular to one another?

Solve simultaneously to find the points of intersection (if any) of the ellipse with the given curve $4 x^{2}+y^{2}$ $=40$ with $y=-x+5$

Find the center, lengths of semiaxes, foci, slope of the asymptotes, and vertices for the hyperbola. Use three significant digits if rounding is necessary. $\frac{(y+5)^{2}}{49}-\frac{(x-3)^{2}}{25}=1$

Write the equation of the circle $(x-6)^{2}+(y+8)^{2}=144$ in general form.

Find the vertex, focus, focal width, and equation of the axis for the parabola: $2(y+1)^{2}=6-3 x$

Write the equation of the circle in standard form: center at $(0,0)$ , radius $=4$