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

Q: The focus of the parabola y^2 = 4x is at

A:

Q: Classify the graph of the equation 9x2 + 9y2 − 36x + 6y + 34 = 0 as a circle, a parabola, an…

A: Since the coefficients of x2 and y2 are the same and are of the same sign too. So this given…

Q: Find an equation of the parabola whose graph is shown. y Directrix X = 4

A: Equation of directrix is  X=a

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: Find the standard form of the equation of the circle. Center at the origin and containing the point…

A: We have to find the standard form of the equation of the circle   Center of the circle is at the…

Q: Show that the center of the osculating circle for the parabola y = x2 at the point (a, a2) is…

A: We need to show that the centre of the osculating circle for the parabola y = x2 at the point (a,…

Q: Write the equation of a parabola whose directrix is y = 0.25 and has a focus at (-1, - 2.25).

A:

Q: Classify the graph of the equation 25x2 − 10x − 200y − 119 = 0 as a circle, a parabola, an ellipse,…

A: On simplification, we get

Q: Sketch the graphs of the parabolas (a) x² = 12y (b) y² + 8x = 0 and show the focus and directrix of…

A: If we have parabola in the form of  x2 = 4ay, which is a upward parabola    Then equation of…

Q: The equation of a family of parabolas with axis parallel to the y-axis is

A: We will find the equation of family of parabolas with axis parallel to the y-axis .Below find the…

Q: Find an equation of the circle that has a diameter as the distance between the two vertices of the…

A: As per our guidelines, we can answer only one question in a single request. Kindly re-post the other…

Q: Write the equation of a parabola whose directrix is æ 0.25 and has a focus at (1.75, 6)

A: Given, The parabola whose  Directrix is x = 0.25 Focus at 1.75, 6  We have the write the equation…

Q: Find the equation of the directrix of the parabola y=16x.

A:

Q: Use a graphing device to graph the parabola. 8y2 = x

A: Parabola - Parabola is a locus of the points that have equal distance from a fixed point and fixed…

Q: Find the point on the parabola y* = 2x that is nearest the point (1, 4).

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Q: Classify the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola. 25x2 – 10x –…

A:

Q: Determine the Equation of a circle if the center is at (5, - 4) and radius Is V3.

A: Formula -Equation of circle centred at (h, k) and radius r is (x-h)2+(y-k)2=r2

Q: Find the equation of the circle that passes through the origin and has its center at (-4, 3).

A: The standard form of equation of circle with center h,k and radius r  is x-h2+y-k2=r2 . The general…

Q: The line perpendicular to the directrix and passing through the focus of a parabola is called the…

A: Given:

Q: Find the equation of the circle that passes through the origin and has its center at (0, 4).

A: The standard equation of the circle is x-h2+y-k2=r2, where h,k is the center of the circle and r is…

Q: Find an equation for the hyperbola whose graph is below. Q 40

A: As we know that the center of the horizontal hyperbola is the midpoint of the vertices of the…

Q: Find the center and radius of a circle x+y2+2x+10y-4-0

A:

Q: Find equations for two lines through the origin that are tangent to the ellipse a- 8x +y + 3 =0.

A: We are asked to find the equation of two lines that are tangent to the ellipse.

Q: Classify the graph of the equation 4x2 − y2 − 4x − 3 = 0 as a circle, a parabola, an ellipse, or a…

A: The general equation of the curve is, ax2+by2+cx+dy+e=0 where a, b, c, d, and e are the constants.…

Q: Write the equation of a parabola whose directrix is y = 9 and has a focus at ( – 10, – 5). |

A: Given (-10, -5) is the focus and y=-9 is the directrix of parabola. Let x0, y0 be any point on the…

Q: Change y -4x+x +6y=2 into standard form. Identify the graph parabola. as an ellipse, circle,

A: Consider the given equation y2 – 4x + x2 + 6y = 2 We observe that the coefficients of squared terms…

Q: If the intersection points of the hyperbola 3x² – y² = 11 and the line 2x + y = 10 are P and Q,…

A:

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

A:

Q: Use a graphing device to graph the parabola. y2 = -1/3x

A: Use the parametric form of parabola. The parametric form for the parabola of the form y2=-4ax is…

Q: Sketch the parabola and line on the same graph. y = 3x2 − 4  and  y = 2x + 4

A: point out zero of function and line and draw graph using these points

Q: Find the equations of the osculating circles of the parabola y = 3(x – 2)2 at the points (2,0)

A:

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

A:

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: State whether the graph of the equation is a parabola, circle, ellipse, or hyperbola. 4x² – 3x – 8y?…

A: x2-3x-8y2-4y=14 The x2 and y2 terms have different signs and different coefficients. So, it is a…

Q: Determine the equation of the parabola vertex at (-4,-8) directrix is x=0.

A:

Q: The distance between the vertex and the focus of a parabola is called the __________ length and is…

A: First of all, consider the definition of the vertex and the focus of a parabola.The vertex of…

Q: Sketch the parabola and line on the same graph. y = x2 + 4 and y = 2x + 2

A: Given, y=x2+4   y=2x+2  The graph of given functions can be plotted as shown in the figure below.

Q: Write the equation of a parabola whose directrix is y = 7.5 and has a focus at ( – 4, – 4.5). -

A: The equation of parabola whose directrix is y=-7.5 and has a focus at (-4,-4.5).

Q: Find the abscissa of the center of circle with equation 3x^2 + 3y^3 - 21x + 24y = 16

A:

Q: Find the equation of a parabola that has focus at (-4,0) and directrix 2

A:

Q: Write the equation of a parabola whose directrix is x 12.5 and has a focus at (5.5, – 9). -

A:

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: Find the directrix of the parabola.  y^2= -10x

A:

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 an equation of the sphere whose diameter is the line segment having endpoints at (6,2, –5)

A: To find the equation of sphere.