Step-by-step solutions to hundreds of conic sections

Recent questions in Conic sections

Tolnaio 2021-08-11 Answered

Find the equation of the graph for each conic in general form. Identify the conic, the center, the vertex, the co-vertex, the focus (foci), major axis, minor axis, $a^{2}$ , $b^{2}$ , and $c^{2}$ . For hyperbola,find the asymtotes.Sketch the graph
$16 x^{2} - 4 y^{2} - 64 = 0$

tabita57i 2021-08-11 Answered

Find the vertices and foci of the conic section. $\frac{x^{2}}{4} - \frac{y^{2}}{9} = 36$

Wierzycaz 2021-08-11 Answered

Find the equation of the graph for each conic in standard form. Identify the conic, the center, the vertex, the co-vertex, the focus (foci), major axis, minor axis, $a^{2}, b^{2}$ , and $c^{2}$ ?. For hyperbola, find the asymptotes. Sketch the graph. $9 x^{2} + 25 y^{2} + 54 x - 50 y - 119 = 0$

pancha3 2021-08-10 Answered

Show that the graph of an equation of the form
$A x^{2} + C y^{2} + D x + E y + F = 0, A \neq 0, C \neq 0$
where A and C are of opposite sign,
(a) is a hyperbola if $\frac{D^{2}}{4 A} + \frac{E^{2}}{4 C} - F \neq 0$
(b) is two intersecting lines if $\frac{D^{2}}{4 A} + \frac{E^{2}}{4 C} - F = 0$

Efan Halliday 2021-08-10 Answered

Perform a rotation of axes to eliminate the xy-term, and sketch the graph of the “degenerate” conic. $x^{2} + 2 x y + y^{2} - 1 = 0$

nitraiddQ 2021-08-10 Answered

Let A be a symmetric $2 \times 2$ matrix and let k be a scalar. Prove that the graph of the quadratic equation $x^{T}$ Ax=k is ,an ellipse, circle, or imaginary conic if $k \neq q 0$ and det A > 0

nagasenaz 2021-08-10 Answered

Find the equation of the graph for each conic in general form. Identify the conic, the center, the vertex, the co-vertex, the focus (foci), major axis, minor axis, $a^{2}$ , $b^{2}$ , and $c^{2}$ . For hyperbola,find the asymtotes.Sketch the graph
$x + 2 y^{2} = 4$

ossidianaZ 2021-08-10 Answered

Find the equation of the graph for each conic in general form. Identify the conic, the center, the vertex, the co-vertex, the focus (foci), major axis, minor axis, $a^{2}$ , $b^{2}$ , and $c^{2}$ . For hyperbola,find the asymtotes.Sketch the graph
$2 {(y + 2)}^{2} + 4 {(x - 4)}^{2} = 8$

Sinead Mcgee 2021-08-10 Answered

Perform a rotation of axes to eliminate the xy-term. xy+5=0

preprekomW 2021-08-09 Answered

Find the equation of the graph for each conic in standard form. Identify the conic, the center, the vertex, the co-vertex, the focus (foci), major axis, minor axis, $a^{2}, b^{2}$ , and $c^{2}$ ?. For hyperbola, find the asymptotes. Sketch the graph. $y^{2} + 4 y - 2 x + 6 = 0$

kuCAu 2021-08-09 Answered

Use the information provided to write the general conic form equation of each ellipse.
$\frac{x^{2}}{36} + \frac{y^{2}}{81} = 1$

bobbie71G 2021-08-09 Answered

Show that the equation represents a conic section. Sketch the conic section, and indicate all pertinent information (such as foci, directrix, asymptotes, and so on). $(a) x^{2} - 2 x - 4 y^{2} - 12 y = - 8 (b) 2 x^{2} + 4 x - 5 y + 7 = 0 (c) 8 a^{2} + 8 x + 2 y^{2} - 20 y = 12$

floymdiT 2021-08-09 Answered

Find the equation of the graph for each conic in general form. Identify the conic, the center, the vertex, the co-vertex, the focus (foci), major axis, minor axis, $a^{2}$ , $b^{2}$ , and $c^{2}$ . For hyperbola,find the asymtotes.Sketch the graph
${(x - 2)}^{2} + {(y - 1)}^{2} = 49$

lwfrgin 2021-08-08 Answered

Find the equations of the parabolas that share a vertex and a focus with the ellipse. Draw the conics. $25 x^{2} + 9 y^{2} = 9$

usagirl007A 2021-08-08 Answered

Draw the curve of the given equations a. $x^{2} + y^{2} + 6 x - 12 y + 29 = 0$ , b. $y^{2} - w x - 8 y + 10 = 0$

Jaya Legge 2021-08-08 Answered

Find the equation by determining the type of the conic and draw its graph. $25 x^{2} + 9 y^{2} - 100 x + 54 y - 44 = 0$

BolkowN 2021-08-08 Answered

Find an equation of the conic described.Graph the equation.
Parabola; vertex at (0,0); directrix the line y=-3

Trent Carpenter 2021-08-08 Answered

Find the equation of the graph for each conic in general form. Identify the conic, the center, the vertex, the co-vertex, the focus (foci), major axis, minor axis, $a^{2}$ , $b^{2}$ , and $c^{2}$ . For hyperbola,find the asymtotes.Sketch the graph
${(y + 7)}^{2} + {(x - 5)}^{2} = 25$

texelaare 2021-08-08 Answered

Find the equation of the graph for each conic in general form. Identify the conic, the center, the vertex, the co-vertex, the focus (foci), major axis, minor axis, $a^{2}$ , $b^{2}$ , and $c^{2}$ . For hyperbola,find the asymtotes.Sketch the graph
$9 {(y - 3)}^{2} - 4 {(x + 5)}^{2} = 36$

ringearV 2021-08-08 Answered

Find the largest and smallest distances from the origin to the conic whose equation is $5 x^{2} - 6 x y + 5 y^{2} - 32 = 0$ and hence determine the lengths of the semiaxes of this conic.

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