91Ó°ÊÓ

Find an equation of the ellipse that satisfies the oiven conditions. $$ \text { Foci }(\pm 1,0) \text {, length of minor axis is } 2 \quad x^{2}+2 y^{2}=2 $$

For Problems \(31-50\), find an equation of the parabola that satisfies the given conditions. $$ \text { Focus }(5,0) \text {, directrix } x=1 \quad y^{2}-8 x+24=0 $$

Find the equation of the circle that passes through the origin and has its center at \((-3,-4)\). \(x^{2}+y^{2}+6 x+8 y=0\)

For Problems \(31-50\), find an equation of the parabola that satisfies the given conditions. $$ \text { Focus }(-3,-1) \text {, directrix } y=7 \quad x^{2}+6 x+16 y-39=0 $$

Find the equation of the circle that has its center at \((-2,-3)\) and is tangent to the line \(x+y=-3\).

The point \((-1,4)\) is the midpoint of a chord of a circle whose equation is \(x^{2}+y^{2}+8 x+4 y-30=0\). Find the equation of the chord.

For Problems \(31-50\), find an equation of the parabola that satisfies the given conditions. $$ \text { Focus }(-4,5) \text {, directrix } x=0 \quad y^{2}-10 y+8 x+41=0 $$

For Problems \(31-50\), find an equation of the parabola that satisfies the given conditions. $$ \text { Focus }(5,-2) \text {, directrix } x=-1 \quad y^{2}+4 y-12 x+28=0 $$

Find the equation of the circle that is tangent to the line \(3 x-4 y=-26\) at the point \((-2,5)\) and passes through the point \((5,-2) . \quad x^{2}+y^{2}-2 x-2 y-23=0\)

For Problems \(31-50\), find an equation of the parabola that satisfies the given conditions. Vertex \((0,0)\), symmetric with respect to the \(x\) axis, and contains the point \((-3,5) \quad 3 y^{2}=-25 x, y^{2}=-\frac{25}{3} x\)