Finding an Equation of a Parabola Find an equation of the parabola y = ax? + bx + c that passes through (0, 1) and is tangent to the line y = x – 1 at (1, 0).

Q: 1. A bug crawls on the plane z = 2x +y, from the point (-2, 4, 0) to the point (2, 4, 8) along a…

A: a) Given equation of plane is z=2x+y. Write this equation in the form y=z-2x. The path of bug along…

Q: Draw a diagram to show that there are two tangent lines to the parabola y = x2 that pass through the…

A: First, we find the slope of the parabola at any point x=h. At x=h , y=h^2 So the point is (h,h^2)

Q: Parametric equations and a value for the parameter t are given x = t2 + 1, y = 5 - t3; t = 2. Find…

A: For t=2, x=t2+1=22+1=4+1=5For t=2, y=5-t3=5-23=5-8=-3

Q: FunTrivia B BYJU'S Stu Toppr Consider the parabola given by the equation y = x'2 + 4x - 5. At which…

A: Given:-  y=x2+4x-5   Slope of tangent  is:      dydx=2x+4

Q: Tangent lines for a hyperbola Find an equation of the line x? y? tangent to the hyperbola - = 1 at…

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Q: Consider the parabola y = 5x - x2. (a) Find the slope of the tangent line to the parabola at the…

A: Given parabola:-   y = 5x - x2 To find slope and tangent find derivative first:-

Q: 39. Motion along a parabola A particle moves along the top of the parabola y? = 2x from left to…

A: Given, y2 = 2x, Magnitude of velocity = Constant speed = 5 units per second, Velocity at (2, 2) = ?

Q: Parametric equations and a value for the parameter t are given x = t2 + 3, y = 6 - t3; t = 2. Find…

A: For t=2, x=t2+3=22+3=4+3=7 For t=2, y=6-t3=6-23=6-8=-2

Q: i        Find the y-coordinates of the points of intersection of the parabola with equation y = x2 –…

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Q: Orthogonal trajectories Two curves are orthogonal to eachother if their tangent lines are…

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Q: Which of these are associated with a parabolic equation? a. Neither initial conditions nor boundary…

A: Equation of parabolic equation is heat equation.

Q: 2 (2) The vertex of a parabola is the point where the curvature is highest. For example, the vertex…

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Q: Orthogonal Irajectories A parabola is opening downward, always having a length of latus rectum equal…

A: Given: The given parabola is open downward. It has a length of latus rectum equal to 4, so that we…

Q: 3) From elementary geometry we know that there is a unique straight line through any two points in a…

A: Given: There is a unique straight line through any two points in a plane. There is a unique parabola…

Q: Finding Equations of Tangent Lines Graph the two parabolasy = x2 and y = − x2 + 2x − 5 in the same…

A: Given: y = x2 and y = − x2 + 2x − 5

Q: Find the coordinates of the midpoint of HX -4 The coordinates of the midpoint of HX are L (Type an…

A: We have to find

Q: 4x - x2. Consider the parabola y = (a) Find the slope of the tangent line to the parabola at the…

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Q: Quadratics having a common tangent The curves y = x2 + ax + b and y = cx - x2 have a common tangent…

A: Given curves :             y1 = x2 + ax + by2 = cx - x2That y1 passes through point (1,0).  Thus,…

Q: Find parametric equations for the line. (Use the parameter t.) The line through the points (0,, 1)…

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Q: Parabola vertex property Prove that if a parabola crosses thex-axis twice, the x-coordinate of the…

A: We know that equation of a parabola is, y=ax2+bx+c           ...(1) And the vertex of the parabola…

Q: Find parametric equations for the line. (Use the parameter t.) The line through the points (0,, 1)…

A: Given data- The line through the points (0,1/2,1) and (9,1,-4). We have to find - The parametric…

Q: nsider the parabola y = 7x - x2. (a) Find the slope of the tangent line to the parabola at the point…

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Q: Tangent lines for an ellipse Show that an equation of the line x?, y? a tangent to the ellipse 1 at…

A: Let y=f(x) be a curve We need to find tangent at (x',y') At first we need to find dydx|(x',y')The…

Q: lutions/Independent work 1. Determine the equation of a cubic function with zeros at -2, 1-3, 1+3…

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Q: Another bug on a parabola A bug is moving along the parabolay = x2. At what point on the parabola…

A: Given: A bug is moving along the parabola y=x2. To Find: At what point the parabola are the x-and…

Q: Bug on a parabola A bug is moving along the right side of the parabola y = x2 at a rate such that…

A: Distance between two points x1,y1,x2,y2 is given by the formula x1-x22+y1-y22. Hence, distance of a…

Q: Find parametric equations for the line. (Use the parameter t.) The line through the points (0,, 1)…

A: Parametric equation of line with parameter t . x( t ) = x0 + a t y ( t ) = y0 + b t z ( t ) = z0 +…

Q: Parametric curvesa. Eliminate the parameter to obtain an equation in x and y.b. Describe the curve,…

A: a) Here x=t2+4, y=-t  for -2<t<0we have to eliminate the parameter to obtain an…

Q: Find the equation of the parabola y = ax2 + bx + c that passes through the points. To verify your…

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Q: Finding Equations of Tangent Lines Graph the two parabolas y = x² and y = -x² + 2x – 5 in the same…

A: Given two parabolas, y=x2,  y=-x2+2x-5 Slope of both parabolas, dydx=2x,    dydx=-2x+2…

Q: Find the equation of the tangent line and normal line to the curve y = (4 + 6x)² at the point (4,…

A: Given equation of curve is We know that slope of tangent line to curve y=f(x) at x=a is f'(a).…

Q: Consider the parabola y = 7x - x2. (a) Find the slope of the tangent line to the parabola at the…

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Q: Parametric equations for the line through (5, 3, 7) and parallel to the line x = 3−t, y = 2, z = 8 +…

A: Known fact: The equation of line passing through x1, y1, z1 and parallel to the line x=x2+at,…

Q: Analytic Geometry:  Trace the curve y2 = (x − 1)(2x + 3)(3x − 1).

A: To trace the curvey2=x-12x+3(3x-1)

Q: (equation of the parabola) Parabolas with axis parallel to the x-axis (result of elimination of…

A: We will consider the general equation of all parabolas and then we will eliminate the constants.

Q: a) Find the equation of the tangent line to the parabola at the given point. y = −4x2,  (3, −36)…

A: Given: a) y = −4x2,  (3, −36)   To find: The equation of the tangent line to the parabola at the…

Q: 3. A point describe parabola y = 4x + 1, with a constant velocity, vy = 4. Find vx and ax at point…

A: vx=dxdy= velocity of x with respect to(w.r.t.) yax=d2xdy2= acceleration of x w.r.t. yTo get dydx…

Q: Find parametric equations for the line. (Use the parameter t.) The line through the origin and the…

A: Find parametric equations for the line. The line through the origin and the point (6,4,-1). Find the…

Q: Consider the parabola y = 6x – x2. (a) Find the slope of the tangent line to the parabola at the…

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Q: A parabola passes through the points (-4, 10), (-3, 0), (-2, -6), K (-1, -8), (0, -6), (1, 0), and…

A: (-4, 10), (-3, 0), (-2, -6), K (-1, -8), (0, -6), (1, 0), and (2, 10).To Find:a) Determine an…

Q: Relationship between r and r' Consider the parabola r(t) = ⟨at2 + 1, t⟩, for - ∞ < t < ∞,…

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Q: Motion along a parabola A particle moves along the top of the parabola y2 = 2x from left to right at…

A: To find the velocity of the particle.

Q: Question 7

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Q: A particle moves along the parabola y = 2x² – 3x + 5, where x and y are measured in centimeters. The…

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Q: a) The curve with equation y = x + 3x2 is called the Tschirnhausen cubic. Find an equation of the…

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Q: Parameterize the line from (3,0) to (-2,-5) so that the line is at (3,0) at t=0 and at (-2,-5) at…

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Q: PARABOLAS W TH AXIS PARALLEL TO Y- AXIS A) DRAW ILUSTRATION B-) EQUATION OF THE PATA BOLA c) RESULT…

A: Formation of the differential equation

Q: (a) The curve with equation y = x + 3x² is called the Tschirnhausen cubic. Find an equation of the…

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Q: Family of parabolas whose vertex is along the line y = -2, and whose distance from vertex to…

A: let's find.