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

Q: What is the length of the latus rectum (LR) of the parabola y = -÷(x – 2)“ + 5?

A:

Q: Determine the general equation of a parabola opening downwards whose vertex is at (3,-4) with a…

A:

Q: Find the equation in rectangular coordinates of the quadric surfaceconsisting of the two cones φ =…

A: The relation between spherical and rectangular coordinates in polar form is given by the following…

Q: Suppose a and b are positive numbers. Sketch the parabolas y2 = 4a2 - 4ax      and         y2 = 4b2…

A:

Q: There is a parabola which has a minimum where the two lines 3x+6y-1=0 and 2x+ y-2=0 intersect. The…

A:

Q: What is the length of the latus rectum of a parabola having its vertex at the origin and focus at…

A: The length of latus rectum of parabola = 4a

Q: 7. Determine all values of a that will cause the parabola y=ax² +10x+1 to cross the x-axis at two…

A: 7) y=ax2+10x+1 ...................eq (1) For parabola to cross the x- axis put y=0 0=ax2+10x+1…

Q: What is the general equation of a parabola that opens upward with V(-1,2)?

A: The general equation of the parabola opening upwards is x-h2=4py-k where (h,k) is vertex. here…

Q: "What is the families of the curve of all Parabolas with axis parallel to the x-axis

A:

Q: What is the equation of the parabola with axis parallel to the x-axis, whose vertex is at (-1,7) and…

A:

Q: Find the equation of the parabola with directrix x + 1 = 0, axis y = 2, and latus rectum 3.

A: Given :          The equation of directrix of the parabola is x + 1 = 0          The length of the…

Q: A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola y=9−x2…

A:

Q: What is the equation of the directrix of the parabola having a vertex at (6,0), passing through…

A: Given:- What is the equation of the directrix of the parabola having a vertex at (6,0), passing…

Q: Find the equation for the parabola that has its vertex at the 1 origin and has directrix at y 41…

A:

Q: Give 3 points that lie on the parabola y=x^2-5x-2

A:

Q: The point (1,2) lies on the parabola: y 3x2 -2x+2 %3D

A: Thanks for the question :)And your upvote will be really appreciable ;) False statement (1,2) does…

Q: State whether the given equation defines an elliptic paraboloid, a hyperbolic paraboloid, or an…

A: 3x2-7y2=z On simplification, we get ⇒z=x213-y217⇒z=x2132-y2172⇒z=x132-y172

Q: If the coordinates of the ends of a focal chord of the parabola y²=4ax and (x,,y,) and (x,.y;) then…

A: Consider the given parabola y2=4ax Suppose Ax1 , y1  and  Bx2 , y2 be the ends of the focal chord of…

Q: Find the tangent line to the parabola x2-6y=10 through (3,5) (ILLUSTRATE SOLUTION)

A:

Q: On a separate piece of paper, sketch the graph of the parabola y = x + 3. On the same graph, plot…

A: Given: Equation of parabola, y=x2+3

Q: what is the equation of a parabola with a vertex at (4, 8) and a directrix at y=5

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: Sketch the parabola y = x² + 2x +1. Use arrows to indicate the maximum and minimum values of y over…

A:

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

A: Here we find the equation of parabola.

Q: Graphically, parabolas can be viewed as the set of all points whose distance from _____ is equal to…

A: Graphically, parabolas can be viewed as the set of all points whose distance from _____ is equal to…

Q: The area bounded by the parabola y2 = 4ax, its axis, and its latus rectum revolves  about the x-

A: The given equation of parabola is y2=4ax. The objective is to calculate the area bounded by the…

Q: 1. What is the equation of the line to the parabola y = x2 + 5x +1 through the 15 point at

A: Given, Parabola  y=x2+5x+1 Point 12, 154

Q: Find equations of both the tangent lines to the ellipse  x2 + 7y2 = 63  that pass through the point…

A: consider (x0 ,y0) be an any point on ellipse

Q: What are the coordinates of the end points of the latus rectum of the parabola with equation a - 2z…

A: What are the coordinates of the end points of the latus rectum of the parabola with equation…

Q: Show that the line b2xx1 - a2yy1 - a2b2 = 0 is tangent to the hyperbola b2x2 - a2y2 - a2b2 = 0 at…

A: Find dy/dx.Then find dy/dx at the point (x1,y1) by plugging x=x1 and y=y1

Q: If tangent lines to the hyperbola 9x2 − y2 = 36 intersect the y-axis at the point (0, 6), find the…

A:

Q: Find the standard equation of a parabola if its latus rectum measures 9 units, axis at y = 3, p is…

A: Let's find standard equation of a parabola.

Q: the center-radius of the equationn 9x²-18 x+ 9+9y? + 12y=12 be obtained by adding both sides of the…

A:

Q: Determine the coordinates of points A and B on a parabola y midpoint of AB is as close as possible…

A:

Q: Find the equation of the parabola with directrix x + 1 = 0, axis y = 2, and latus rectum 2.

A:

Q: Find the minimum distance between the point (5,1) and the parabola y=-x2 ?.

A: Find the minimum distance between the point (5, 1) and the parabola y = -x2?

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: ress 3x² + y² + 2z² + 6x – 4y

A: Given,            3x2+y2+2z2+6x-4y-12z+26=0

Q: What point on the parabola y = 3- x² is closest to the point (3,3)? The point on the parabola y = 3…

A:

Q: Explain why a line in hyperbolic geometry must contain two distinct ideal points.

A: We have to answer given Questions.

Q: Show that,the area bounded by the parabola y^2 =4ax and a double ordinate is two third of the…

A: Let the parabola be y2=4ax Also let x =b be any double ordinate.Since the curve is symmetric about…

Q: What point on the parabola y = 1-x is closest to the point (1,1)? The point on the parabola y = 1-x2…

A:

Q: Find the equation of the parabola with directrix y = 3, axis x = 0, and latus rectum 4

A: Given: Equation of directrix:y=3……1Equation of axis:x=0……2Length of latus rectum:4……3

Q: Find the equation of the parabola with directrix x + 2 = 0, axis y = 4, and latus rectum 4.

A:

Q: The parabolic antenna has an equation of y^2 + 8x = 0. Determine the length of the latus rectum.

A: Here we use the standard form of parabola.

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

A: We have to find

Q: Suppose the axis of a parabola is parallel to the yy-axis and passing through the points (0,3),…

A: Given that, the axis of a parabola is parallel to the y-axis. Let the Vertex of the parabola (h, k)…

Q: Find the point(s) on the ellipse 4x² + y² = 4 that are farthest from the point (1,0).

A: We need to find the points on the ellipse that is farthest from the given point. According to first…