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

Q: Consider the curve defined by the equation 2x + y = 3xy for questions (4-6). %3D 2 1 -3 -2 -1 1 2 3…

A: The given curve is: 2x3+y3=3xy

Q: Find the focus and direcctrix of a parabola whose equation is of the form Ax2 + Ey = 0, A ≠ 0, E ≠…

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Q: Discuss and trace the curve of the following equation. 2. y = x+3 у %3D 1. у %3D x²-16

A: The general form of a polynomial function is given by a0xn+a1xn-1+···+an, where a0, a1,···,an are…

Q: Question 9. 20 Jerry kicks a soccer ball which follows a parabolic trajectory given by: y = -x² +x…

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Q: QUESTION 5 Compare (in words) the graphs of y>-4x - 2 For the toolbar, press ALT+F10 (PC) or…

A: solution of the given problem is below ..

Q: Derive the equation of the parabola with a focus at (-7, 5) and a directrix of y = -11. O (x)= (X +…

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Q: The cartesian equation of the curve x = VE .y 1-t is :

A: The characterstics eqaution of the curve is

Q: Consider the curve y = 3x3, The sketch of the portion of this curve between x = - 1 and x = 8 is…

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Q: Find an equation for the curve traced by the point P(x, y) if the distance from P to the vertex of…

A: First find the vertex and focus of x^2=4y

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: Question 7 What is the x-intercept of the following equation: y = 1/2x+ 1 A) (-2,0) None of the…

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Q: NOTE: Solve this as soon as possible, I need this urgently. If tangent lines to the ellipse 9x² +…

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Q: 1. Find the equation of the circle whose center is (1,-1) and which passes through the center of the…

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Q: QUESTION 13 Write the equation of the line that passes through the point P(4, 3) and is…

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Q: The graph, when the curve y=v(3+ x^2 ) from x = 0 to x = 4 is rotated about x - axis is ....

A: This question can be solved using the concept of volume of solid generated when curve is rotated…

Q: 1 - Sketch the curve : y=-(x3– 6x²+9x+6). 6 y=Lcx³-

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Q: Find an equation of the line which is tangent to the circle z + y - 4x + 6y – 12 = 0 at the point…

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Q: The graph of the curve described by the paramnetric equations x = 3t – 4, y = 6t + 2 is a straight…

A: Consider the curve  x=3t-4,y=6t+2

Q: Find the y-intercept of the tangent to the ellipse x + 3y = 1 at the point %3D 1/2

A: We differentiate both sides with respect to x and then solve for dy/dx

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

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Q: Find the focus and directrix of a parabola whose equation is of the form Ax² + Ey = 0, A + 0, E # 0.

A: Explanation: Given that,  Parabola equation is; Ax2+Ey=0, A≠0, E≠0   Write the equation in the…

Q: (금, 용) The graph of a parabola passes through the points (0, 1) and G2) and has a horizontal tangent…

A: We have to find equation of Parabola.

Q: QUESTION 12 What is the y-intercept for h(x) = 4x2+5x – 6? O A. (0, -6) B. (0, -5/4) OC. (0, 5) O D.…

A: y- intercept is given at x=0

Q: 3. Find the equation of the parabola with focus at F(3,2) and with the line x = -4 as directrix.

A: Topic- equation of parabola from focus ans directrix.

Q: 8. Eliminate the parameter to find a Cartesian equation of the curve: x(t) = t, and y(t) = 3t+4, t≥…

A: To eliminate the pararmeter to find a Cartesian equation of the curve: xt=t, and yt=3t+4, t≥0.To…

Q: The graph, when the curve y = √3 + x² from x = 0 to x = 4 is rotated about x - axis is A B C D

A: To find the graph of the solid formed by rotating the given curve about x axis, first we find the…

Q: QUESTION 6 Find in the form y = mx + c the equation of the line 3- -2, 432-1 2 3 -2- -3-

A: Here we have to find the equation of the line in the form of y=mx+c  where m is the slope and c is…

Q: In Problem,determine which of the given points are on the graph of the equation.

A: We know that, a point (a, b) is in the graph of a function f(x) if and only if f(a)=b. We will be…

Q: 2x +2y +4 + 8y + 2 = 0 is the equation of a circle with center (h, k) and radius r for: h and and

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Q: Question 3 5 Find the point symmetric to about the y-axis. 2'6 5 2л 2' 3 b) O 5, 5 5л c) O 2' 6 d) O…

A: Given point is 52,π6We know that if a point (x,y) is symmetric to Y-axis means it will be mirror…

Q: Question 17 Find the point on the parabola y= - x¯ whose tangent line is parallel with y= 3x-5 +4 3…

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Q: Question 14 Find an equation of the line through the point (3, -5) and parallel to the line y 5x-2.…

A: Answer:   given line is passing by two points ( x1, y1)  and parallel to a line ,  :

Q: Question: 08 Determine i. Concavity of parabola ii. Its y intercepts iii. The co-ordinate vertex iv.…

A: we are given a quadratic equation  f(x)=x22-10x

Q: FInd the equations of the tangents with slope m=-2/9 to the ellipse 4x^2+9y^2=40

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Q: The figure below shows a lamp located three units to the right of the y-axis and a shadow created by…

A: Here we need to calculate equation of tangent line on given ellipse which passes through (-5,0)  If…

Q: Find the intersection point(s) of the curves whose equations are: 5x - 4 %3D 2x - 4x + 22 The…

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Q: The equation of the line touching both the parabolas y = 4x and x' =-32y is x-2y+1 = 0, then a is

A: Introduction :

Q: Given a focus of (4,5) and a directrix of y=-3, fınd the equation of the parabola. y = (x –

A: We need to find equation of parabola.

Q: Question 16 There are two distinct lines passing through (-3/2, –3) that are tangent to the parabola…

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Q: Question 23 Which equation represents the parabola shown in the accompanying graph? (-3, 1) A f(x) =…

A: The vertex of the parabola is: (h, k) = (-3, 1)

Q: Find an equation of the parabola that satisfies the given conditions.Focus F(6, 4), directrix y = -2

A: Given: Focus F(6,4) directrix y=-2 To find: the equation

Q: The general equation of the circle that passes through the points (-3,4), (2,–6), and (5,0) is x2 +…

A: Given: Let us consider the given general equation of the circle, x2+y2+Dx+Ey+F=0 and the circle…

Q: Reflect Point C over the y-axis: A 3 -5 -4 -3 -2 -1 5 -1 O a) (-3, 2) O b) (3,2) O d) (3,0) c)…

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Q: 1. Find the Cartesian equation of the curve represented by x = 4t + 3 and y 16t - 9, -0 <t<o.

A: Try to eliminate 't' to establish relation between x and y.

Q: Find an equation in x and y whose graph contains the points on the curve C. Sketch the graph of C,…

A: The given parametric curve is, x=2ty=8t3-1≤t≤1 From the parameter of x, x=2tt=x2

Q: What is the maximum vertical distance between the line y = x + 2 and the parabola y = x ^ 2, for −1…

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Q: 1) Find the intercept(s) and vert ex of the parabola. y=x^2-1

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Q: Question 32 Write an equation for the parabola. 10y 3,6) (0,0) + -10 -8 -6 -4 8. -2 -2 10 x -4 -6+…

A: equation of parabola

Q: Question 5 Find the length of the curve. +- from y = 1 to y = 2 %3D 4y2 2

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Maximization

Have you ever seen a bridge in the shape of a parabola? Where is its maximum on the bridge? The maximum of that bridge is the highest point on that bridge. The process of finding the maximum of the bridge here is called the maximization.