(2) Find the equation of the tangent line to y = when x = = 0. 2+ 33 (3) Find the parabola with equation y = ax2 + b whose tangent line at (11, 10) has equation y = 3x – 23. ***Show all work in finding a and b. Your answer will be the equation of the parabola with a and b filled in. %3D

Q: Find the equation of the line tangent to the ellipse x + 3y 19 at the point (4,1). (Type an…

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Q: 5. Find the maximum and minimum values f(x, y) = xy can take on the ellipse 4x²+y? = 16.

A: The given function f(x,y)=xy to the ellipse 4x2+y2=16

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Q: A quadratic curve y= ax² +bx+c passes through the points (–1,4),(1,–5) and (3,5). Find the equation…

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Q: Find the maximum and minimum values of the function f(x, y) = xy on the ellipse given y? by the…

A: According to the given information, it is required to find the maximum and minimum value of the…

Q: 1 Find the equation for the parabola that has its vertex at the origin and has directrix at y = 13…

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Q: 10. Which is the equation of a hyperbola with co-vertices at (0, 7) and (0,-7) and a transverse axis…

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Q: P(0, -1) from the point (x) = x² + 2x Apses of the points where the tangents drawn on the parabola…

A: The given equation of the parabola is, fx=x2+2x Apses of the points means that two lines meet at…

Q: The parabola y=(x-)+1 has its fous at (2-3). 76 Determine and State of the the equation directiex.

A: Consider the equation of parabola: y=-116x-22+1To   solve,y-1=-116x-22x-22=-16y-1…

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: If a person shoots a basketball overhand from a position 8 feet above the​ floor, then the path of…

A:

Q: Find a parabola with equation y = ax + bx +c that has slope 7 at x = 1, slope -25 at x = -1, and…

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Q: A parabola has an equation of y² = 8x. Find the equation of the tangent to the parabola having a…

A: Use equation of tangent line of parabola and put value

Q: 1. Find the slope and the equation of the tangent line to the curve y=x³ at x=-1 2. Find the slope…

A: Let's find.

Q: 16.) A woodland jumping mouse hops along a parabolic path given by y=-0.2x+ 1.2r where x is the…

A: We will find the maximum value of y, which will represent the maximum height that the mouse can jump

Q: Find the maximum and minimum values of the function f(x, y) = xy on the ellipse given. y? by the…

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Q: 5) Find the equation of a parabola with focus F(7/2,3) and directrix line ==1/2. *

A: We shall use focus-directrix property to solve this problem. This property says, the distance…

Q: Finally, determine a. The parabola passes through the point (0, 5). Substitute the values of x and y…

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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: The line y = 8.5x+5 intersects the parabola (y-4) = (x-6)2 at points A and B. Point C is on the…

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Q: Tangent to a parabola Does the parabola y = 2x2 - 13x + 5have a tangent whose slope is -1? If so,…

A: Given :           The equation of parabola is y = 2x2 - 13x + 5.   To find the equation of tangent…

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

A: It is given that the Vertex is V(0, 0) The focus is on the positive x axis, 2 units away from the…

Q: 17. Two parabolas have functions given by f(x) = -.5z? + 2x + 4and g(r) = 3z2 + 4x + 2 Find the…

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Q: A parabola is opening downward, always having a length of latus rectum equal to 4. The vertex of…

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Q: 3. All vertical parabolas. Ans: y" = 0

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Q: 4.Find the equation of the ellipse with foci (0, = 8) and with endpoints (0,+ 10) 5. Is f(x) = x +1…

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

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: 3. Find an equation of the hyperbola having foci at (4, 3-V 52) and (4, 3 +/52) and asymptotes at y=…

A: Focii: (4, 3+52) & (4, 3-52)Assymptotes : y=3x2-3 , y=-3x2+9Let vertex by represented by (h,k)…

Q: 5.Find the point on the parabola x? = 4y nearest to (0,4).

A: Given:      x2 = 4y    Point : ( 0 , 4 )

Q: find the general equation of the parabola with horizontal axis which crosses the x-axis at x=2 and…

A: To find the general equation of the parabola with horizontal axis which crosses the x‐axis at x=2,…

Q: 2 ax +bx + c that has 1, slope -8 at x -1, and passes through 70. Find a parabola with equation y…

A: We first find slope y' at x.

Q: 1. Which Is the corresponding equation of a hyperbola with co-vertices at (0, -6) and (0, 6) and a…

A: Given, The co-vertices of the hyperbola are 0, -6 and 0, 6  and transverse axis is 20 units long.…

Q: shortest distance from the point (0,6) to the parabola x² – 4y = 0.

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Q: Find an equation of the hyperbola with vertices (0,+-9) and asymptotes y=+-x/3

A: Given

Q: 1. The straight line in the figure is tangent to the parabola. Find the value y = za2 - 4x + 10 6.…

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Q: Ellipses

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Q: Find an equation of the tangent line to the hyperbola defined by (5x^2)+(4xy)−(2y^2)−4x=195 at the…

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

A: Given:

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

A: Consider the given function: y=7x-x2 (a) Slope of the tangent line of a function is derivative of…

Q: 3. Find equations of both the tangent lines to the ellipse x²+4y?=36 that pass through the point…

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Q: Not so long ago, you learned in this course that the vertex of the parabola y = ax? + b bx + c…

A: iven equation of parabola, Y= ax2 + bx +c

Q: Scattering experiments, in which moving particles are deflected by various forces, led to the…

A: Given: y=x2

Q: If a person shoots a basketball overhand from a position 8 feet above the floor, then the path of…

A: The quadratic equation always represent a parabola.

Q: Find an equation of a parabola with focus at (−2,0) and with directrix x=9(Express your answer in…

A: Given that the parabola has the following details:

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 parabola has a vèrtex at the origin and a focus of (0, 3/2). What is the equation of the parabola.

A: The general equation of a parabola with vertex at origin is given by y2=4ax. The distance between…

Q: 2 The parabola y = x + 9 has two tangents which pass through the point (0, – 6). One is tangent to…

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Q: Find the standard form of the equation of the parabola with the given characteristic(s) and vertex…

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Q: Consider the parabola y = 8x - x2. (a) Find the slope of the tangent line to the parabola at the…

A: The given problem for slope of tangent to the curve is solved below in detail.