91Ó°ÊÓ

Find an equation of the parabola that satisfies the given conditions. vertex \(V(1,-2),\) focus \(F(1,0)\)

Find an equation for the ellipse that has its center at the origin and satisfies the given conditions. eccentricity \(\frac{1}{2}\) vertices on the \(x\) -axis, passing through (1,3)

Exer. \(17-26:\) Find an equation for the conic that satisfies the given conditions. hyperbola. with vertices \(V(0,\pm 6)\) and asymptotes \(y=\pm 9 x\)

Find an equation for the hyperbola that has its center at the origin and satisfies the given conditions. $$ \begin{aligned} &\text { foci } F(0,\pm 5)\\\ &\text { conjugate axis of length } 4 \end{aligned} $$

Find an equation of the parabola that satisfies the given conditions. vertex at the origin, symmetric to the \(y\) -axis, and passing through the point (2,-3)

Find an equation for the ellipse that has its center at the origin and satisfies the given conditions. \(x\) -intercepts \(\pm 2, \quad y\) -intercepts \(\pm \frac{1}{3}\)

Find an equation for the ellipse that has its center at the origin and satisfies the given conditions. \(x\) -intercepts \(\pm 2, \quad y\) -intercepts \(\pm_{3}^{1}\)

Find an equation of the parabola that satisfies the given conditions. vertex \(V(-3,5)\), axis parallel to the \(x\) -axis, and passing through the point (5,9)

Exer. \(17-26:\) Find an equation for the conic that satisfies the given conditions. ellipse, with foci \(F(\pm 2,0)\) and passing through the point (2. \(\sqrt{2})\)

Find an equation for the hyperbola that has its center at the origin and satisfies the given conditions. $$ \text { vertices } V(\pm 4,0), \text { passing through }(8,2) $$