5. (a) How do you test whether the graph of an equation is symmetric with respect to the (i) x-axis, (ii) y-axis, and (iii) origin? (b) What type of symmetry does the graph of the equation xy² + y°x² = 3x have?

Q: Which of the following equations is the equation of tangent to the parabola y2 = 2x + 8 at point…

A: The given equation of parabola is: y2=2x+8

Q: 5. Find the equation of the parabola in standard form with a directrix located 5 units below the…

A: equation of the parabola  x-h2=4ay-k

Q: 2)Find the points on the curve y = 2x3 + 3x2 − 12x + 9 where the tangent line is horizontal.

A: As per our guidelines we are allowed to answer only one question. Kindly repost the other question…

Q: 16 In general conic form, what is the equation of the circle whose center is at the origin and…

A: The general equation of the circel with center (h,k) and the radius r is given by:…

Q: Find a set of parametric equations for the parabola whose equation is y = 9 - x2.

A: Given equation is, y=9-x2

Q: A parabola of y=x^2 has been regraphed and now sits with each side plotted at (-3,5) and (3,5) and…

A:

Q: 6. Find the Equation of the Ellipse whose Vertices and Foci are at (0, ±17) and (0, ±9)…

A:

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: (b) Find an equation for the parabola that has axis x = -1 and passes [3] through the points (4,5)…

A: Directrix is a line which together with a point called the focus defines the set of points that form…

Q: 2. Sketch and identify the graph of the equation a + y? – 2y –- 3 = 0 in 3D.

A: x2+y2-2y-3=0x2+y2-2y+1-4=0x2+(y-1)2=4The equation represents circle in 2D,but a cylinder of radius 2…

Q: (a) find the intercepts of each equation, (b) test each equation for symmetry with respect to the…

A: The given equation is y=x3-4x. Note that at x=0, y=0. Thus, the y-intercept is y=0. Compute the…

Q: 1. Find an equation of the ellipse whose foci are (0, -5) and (0, 5) and whose vertices are (0, -6)…

A: If you like the solution then please give it a thumbs up... The Answer is:           Equation:…

Q: 15 2. Find the equation of a parabola through(-, 2) and (0,–1) whose axis is parallel 4 to the…

A:

Q: Two stations that are 2 km apart receive a sound signal issued from a source located at point…

A: The distance between the point 0,-1 and the point P (x, y) is, d1=x2+y+12 The distance between the…

Q: Find the equation of the parabola with vertex at (2,-1), axis is parallel to the y-axis and passing…

A: Equation of parabola parallel to y axis is given by as: (x-h)²= 4a(y-k)

Q: In Problem,rotate the axes so that the new equation contains no xy-term.Analyze and graph the new…

A: Given: 9x2-24xy+16y2+80x+60y=0

Q: 2. Sketch and identify the graph of the equation a+y? - 2y-3 0 in 3D.

A:

Q: 17. If the focus of the parabola is (-2, 1) and the directrix has the equation x + y = 3 then the…

A: Given Focus of parabola f (-2, 1) Equation of directrix is x+y =3   Here the objective is to find…

Q: 2. f(x) = 2 - 5x + 2x Sketch: Opens: Vertex: Equation for Axis of Symmetry:

A: The quadratic function is f(x)=2-5x+2x2 Let the function of the form f(x)=ax2+bx+c, if a > 0 then…

Q: 4. The equation of a family of circles with center an the y-axis is 5. The equation of a family of…

A: Topic:- geometry  Note:- as per our guideline if more than one question uploaded than only first…

Q: 1. Write the standard equation for the ellipse whose minor axis is the line segment from (0, -2) to…

A:

Q: 1) Graph 3x* +8у? %3D72 Also graph the foci.

A:

Q: Find an equation for the parabola that has its vertex at the origin and satisfies the given…

A: We have Vertex=(0,0)Directrix x=-15

Q: Find equations for the osculating circles of the parabola y=0.5x2 at the points (0,0) and (-1,1/2).

A:

Q: Pick one of the equation a or b from Question 3 to graph the parabola. Indicate x- intercepts, y-…

A: Parabola equation is y = 16x2 - 1. Graph:

Q: 9 2x – 5xy + 2y?

A: When a conic contains xy term which means coordinate axis rotated about an angle θ .Suppose the…

Q: 5. Find the equation of the parabola that has a horizontal axis of symmetry, passing through the…

A: the general equation of a parabola is x=ay2+by+c                            (1) horizontal axis…

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

A:

Q: Find two solutions of y = x - 4 38 Point 1: (2, y) Point 2: (x, y) → Then graph: 51 4 3 2 4 5 -5 4…

A:

Q: Another constraint you can use to compute cubic splines is that the second derivatives of adjoining…

A: Consider the cubic polynomial  fx=⋮ai-1x3+bi-1x2+ci-1x+di-1, x∈(xi-1,xi]aix3+bix2+cix+di…

Q: (3) Find the coordinates of the points of intersection of the parabola y = x2 - ax and the line y =…

A:

Q: What is an equation of the axis of symmetry of the graph of the parabola y = 2x² + 3x + 5? A y=-} O…

A:

Q: 4x^2 - 3y^2 + 12z^2 + 12 = 0

A:

Q: How do you find the standard form of the equation of the parabola with the given characteristic(s)…

A: Given vertex is at origin i.e (h,k) = (0,0) To find the standard equation of parabola

Q: 4. Find the equation of a parabola with axis parallel to the y-axis and passing through ( ). G. 3…

A: According to our guidelines, In case of multiple questions we are supposed to answer the first…

Q: 1. Consider the parabola whose directrix is at x = -7 and whose focus is at (-1, 1). What is the…

A:

Q: 1. Determine the equation of the parabola whose vertex is at the point (-1, –1) and whose directrix…

A: We have to determine the equation of the parabola whose vertex is at the point (-1,-1) and whose…

Q: Question 6 In the xy-plane, what is the y-intercept of the graph of the equation y = V4 -T?

A: Let's find.

Q: Find a parabola with equation y=ax^2+bx+c that has slope 4 at x = 1, slope -8 at x = -1, and passes…

A:

Q: 5. Find the equation of the parabola in standard form with a directrix located 5 units below the…

A: The standard equation of the parabola is (x-h)2=4a(y=k) Where (h,k) is the vertex Here h=3, k=-2…

Q: Two large airship hangars were built in Orly, France, in the early 1900s but were destroyed in World…

A: (a). It is given that, the length of hangars is 175 m, the width of the hangers is 90 m and the…

Q: Find the equation of a parabola whose focus is at(2,-3) and directrix's equation is x=5.

A: Distance between the point x1 , y1 and a lineax+by+C=0 is ax1+by1+Ca2+b2

Q: 9. Find equations for two lines through the origin that are tangent to the ellipse 1² – 4x + 4y² =…

A: We have to find

Q: find the orthogonal trajectory of family of parabolas represented by the equation…

A: To find orthogonal trajectories of  y2=4ax.

Q: 3) Find the equation for the ellipse that has vertex at (9, -1) and foci (0, -1) and (8, -1).

A:

Q: Which is the equation of an ellipse with direcrices at x = =-4 and foci at (2,0) and (-2,0)

A: Center is the midpoint of the foci  midpoint of (2,0) and (-2,0) is : Directrix = -4

Q: 1. Express the following equation in vertex form: y coordinates of the vertex point. 2 = 3x² 12x +…

A:

Q: 7) Find the standard form of the equation for the parabola with vertex (1,2) and directrix y -1.

A: