Reduce each equation to a standard form and describe the curve completely. If the curve is a: CIRCLE- supply the center and radius PARABOLA- supply the direction of the opening, vertex, focus, ends of latus rectum ELLIPSE- supply the center and direction of major axis, vertices, foci, ends of latera recta, directrices HYPERBOLA- supply the center and direction of transverse axis, vertices, foci, ends of latera recta, directrices, and asymptotes.

Q: Find the standard form of the equation of a circle with center (-1,1) and radius v2. Graph the…

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Q: find a cartesian equation for the curve r2 = 14

A: Find a cartesian equation for the curve         r2 = 14

Q: Find the standard equation of all circles having center at a focus of 52 7(x+2)? (y-3)2 = 1 39 and…

A: Let's find.

Q: find the standard form of the equation of each circle. Center (2, 3) and tangent to the x-axis

A: Given: The center of a circle is (2,3) and tangent to the x-axis.

Q: 1. Find the center and radius for each equation of a circle. (x+ 5)2 + (y - 1)2 = 49 %3D Center (

A: Solution; Consider the given equation of the circle: x+52 + y-12 = 49 Comparing the given equation…

Q: Identify the family of curves of an ellipse if the foci are located on the y-axis and centre of the…

A: Equation of an ellipse with foci on y axis and center at origin is given by  x2b2+y2a2=1…

Q: the points where the curve meets the axes.

A: y= (x-2)(x+1)(x+2) When x=0, y=-4 When x=1, y=-6 When x=-1, y=0 When x=2, y=0 When x=-2, y=0 When…

Q: Find an equation of the parabola whose graph is shown. y Focus

A: In this problem , parabola symmetric about y - axis . Vertex form of parabola if symmetric about y -…

Q: find the standard form of the equation of each circle.   Center at the origin and containing the…

A: Center of the circle is origin and it contains the point -2, 3. Equation of the circle with center…

Q: Identify the curve by finding a Cartesian equation for the curve r = 4secθ

A: The given curve is,

Q: Name the type of basic curve that each pair of equations represents (lines, parabolas, circles,…

A: Given data:     The first given equation is: y=3sin(t). The second given equation is: x=3cos(t).…

Q: For each curve in Figure 31, state whether it is symmetric with respect to the y-axis, the origin,…

A: To state whether it is symmetric with respect to the y-axis, the origin, both, or neither.

Q: Graph each ellipse. Identify the center, vertices, co-vertices, length of major axis, length of…

A: x-1216+y-424=1 x-1242+y-4222=1 compare this equation with the standard equation of an ellipse…

Q: find the standard form of the equation of each circle.   Center 1 - 3, 12 and tangent to the y-axis

A: Center of the circle (-3,12)

Q: A satellite is in elliptical orbit around the earth with the center of the earth at one focus. The…

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Q: Find the equation of the circle with center at (4. -1) and passing through the point (2. -2).

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Q: find a Cartesian equation of the curve

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Q: Reduce the equation to a standard form and describe the curve completely by providing the important…

A: The given equation is 2y2+x+8y-4=0. Rewrite the equation in standard form:…

Q: Indicate whether the following equations define a straight line (L), a circle (C), an ellipse (but…

A: Concept of identifying the equation Circle for the equation of circle, both x and y are squared…

Q: Find a Cartesian equation for the curve and identify it as either a hyperbola, circle, limaAson,…

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Q: Identify the center and radius of the circle with the given equation in each item. Sketch its graph,…

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Q: (b) Find a rectangular-coordinate equation for the curve by eliminating the parameter.

A: Given equations in the parametric form as:x= cos2(t), ............................(1)y = sin2(t)…

Q: Determine whether the curve 16x² - 9y² + 144 = 0 is a circle, parabola, ellipse or hyperbola.

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Q: Reduce each equation to a standard form and describe the curve completely by providing the important…

A: 1  x2+y2+6x+8y=-9

Q: Eliminate the parameter to find a Cartesian equation of the curve.

A: Given  x=sin(t)  y=csc(t) and 0<t<π/2 We need to find the Cartesian equation and graph

Q: find the standard form of the equation of each circle.   Center 12, 32 and tangent to the x-axis

A: we have to find the standard form of the equation of each circle with center (12, 32 )  and tangent…

Q: Reduce each equation to a standard form and describe the curve completely by providing the important…

A: Step:-1 Given that 3x2−2y2−12x+12y=12 It can be written as…

Q: Reduce each of the following equations to standard form then sketch the graph of each. If the…

A: Explanation of the answer is as follows

Q: 3x2 – 2y2 – 12x + 12y = 12

A: Given equation : 3x2-2y2-12x+12y=12

Q: Find a Cartesian equation for the curve and identify it as an ellipse, circle, limAson, parabola, or…

A: Cartesian equation for the curve is r = 3 cos(θ) Now x = r cos(θ)   ……(1)

Q: Given the equation 6x2 + 9y2 = 1 Name the curve that is the graph of the equa Name of the curve:…

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Q: b) An ellipse is a circle if and only if a - b = Find the equation of the parabola whose focus is…

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Q: The graph of the equation  (x − 4)2 + (y − 2)2 = 9  is a circle with center  (x, y) =    and…

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Q: Find the focus and directrix of the parabola y = -x2, and sketch the graph.

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Q: Determine the equation of the parabola given the focus at (-10,23/2) and directrix at y=-11/2.…

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Q: 4. Convert the equation r =8cos0– 2sin0 to Cartesian coordinates and fully describe the resulting…

A: see below the answer

Q: Find the standard form of the equation of the circle having the following properties: Center at the…

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Q: Find the equation of the circle passing through this point (5,1), (3,-1) with the centre on the…

A: Consider that the circle passes through point (5,1) and (3,-1) with center on y-axis.   The equation…

Q: Determine whether the curve 12x² + 3y² = 36 is a circle, parabola, ellipse, or hyperbola.

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Q: Graph the ellipse and indentify the following (x+22 . v+5)2 1) Domain: 16 4 Range: Foci: +++ 10 X…

A: Follow step 2

Q: Identify the type of curve given by each equation. r = 4 + 13sin 0 Cardiod Limacon Circle Lemniscate

A: A cardioid is a heart-shaped plane figure. It is a curve which is defined as the locus of a point…

Q: Find the focus, directrix, and focal diameter of the parabola y = x², and sketch its graph.

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Q: 3x2 – 2y2 – 12x + 12y = 12

A: Given that, The given equation of a curve is 3x2-2y2-12x+12y=12. First, we have to convert it into…

Q: (x-1), (v+3) +. =D1 4 6.

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Q: Use the information provided to write the vertex form equation of each parabola. 2) Vertex at…

A: here we have vertex:0,0,    focus:0,18 here x-coordinate is the same for both points so the parabola…

Q: Find the vertex focus focal width and equation of the axis for each parabola. y^2+8y+4-6x+0

A: Given: y2+8y+4-6x=0 for finding given values, first we convert given equation in standard form of…

Q: Determine the equation and sketch the graph the parabola given focus at (12, 3) and directrix at x =…

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Q: Find the equation of the general circle that touches the axes of the two points (-0.3,0) , (0,0.3)

A: Equation of circle

Q: find a cartesian equation for the curve r=3cos(θ)

A: Cartesian equation for the curve is r=3 cos(θ)   Now x=r cos(θ)  …….. equation(1) cosθ=xrr=3xcosθ…