The focus of the parabola defined by the equation x2 = 20 y is %3D (4, 5) (0, 0) O A. В. (0, 5)| (0, – 5) Ос. O D.

Q: Determine the value of p (where Ip| corresponds to the distance from the vertex to the focus) of the…

A: Given: Vertex of parabola is 3, -6and y-intercepts are 0, -10 and 0, -2. To determine: Value of p.

Q: Find the coordinates of the vertex of the parabola y = x^2 - 4x + 1 using derivatives O (2, -3) O…

A: To find the vertex of the parabola by using derivatives

Q: Find the equation of the Hyperbola whose Foci are at (6,4) and ( 30,4),and the length of its…

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Q: Find a function whose graph is the lower half of the hyperboloid -x2 - y2 + z2 = 1.

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Q: Find the equation of the line tangent to the hyperbola x + 2xy - y + x = 5 at the point (3,7)

A: Given,            x2+2xy -y2+x =5 and point (3,7)

Q: Derive the equation of the parabola with a focus at (0, 1) and a directrix of y = -1. f(x) 4 O (x) =…

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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: 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: Find the focus of the parabola y2 - 8x + 4y + 28 = 0. Select one: O a. (5, - 2) O b. (3, - 2) O c.…

A: We have to find the focus of the parabola

Q: Find the points on the curve x^2y = 2 nearest the origin.

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Q: Derive the equation of the parabola with a focus at (2, 4) and a directrix of y = 8. 1 O f(x) -(x –…

A: Given query is to find the equation of parabola.

Q: Where does the line x = 1 + 3t, y = 2−t intersect (a) the x-axis (b) the y-axis (c) the parabola y =…

A: Parametric equations are a set of equations where 2 or more variables are dependent on one single…

Q: Find the value of Y for the hyperbola defined by the equation y² – x² = 7 at the point (3, 4). dx2

A: The equation is y2-x2=7. First find the value of dydx as follows.…

Q: Show that line d:3x-4y-5=0 is tangent to hyperbola H:x2-4y2=5 and find the point of contact of the…

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Q: What is the equation of a parabola in standard form with vertex V(3, – 3) and focus F(3, 2)? A (x-…

A: NOTE: Refresh your page if you can't see any equations. . the vertex is at  and the focus is at

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: find the equation of the parabola y = ax? + bx + c that passes through the points. (0, 3), (1, 4),…

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Q: Find the point(s) on the hyperbola x^2 - y^2 = 2 closest to the point (0, 1).

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Q: Consider the graph of  y = ax2 + bx + c, where a = -3, b = 2 and c = 1.  Is the parabola concave up…

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Q: Find the equation of the tangent to the hyperbola x2 - 4y2 = 9 at (5, 2).

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Q: Find b and c, given that the parabola y = x2 + bx + c passes through (0, 5) and (3, 23).

A: (0,5) means when x=0 then y=5. similarly, (3,23) means when x=3 , then y=23.

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

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Q: Show that the number 4p is the width of the parabola x2 = 4py (p>0) at the focus by showing that…

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Q: find the points on the parabola y=x^2 closest to the point (0,1)

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Q: How far from the x axis is the focus of the hyperbola (x^2)- (2y^2) + 4x + 4y+ 4 = 0?

A: the given equation of hyperbola is  x2- 2y2+4x+ 4y + 4 =0 it is asked to find how far is focus of…

Q: In the figure to the right, the equation of the solid parabola is y=x² – 14 and the equation of the…

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Q: Find the point in the parabola y2 = 4x at which the rate of change of the ordinate and abscissa are…

A: Parabola is  y2=4x Differentiate the above equation with respect to t ⇒2ydydt=4dxdt. Since…

Q: Find the equation of the line tangent to the hyperbola x2 −y2 =16 at (5,3).   Give your answer in…

A: The line is tangent to the given hyperbola at (5,3).Tangent line is a straight line.Therefore, the…

Q: Find the equation of the asymptotes for the hyperbola (y – 5)2 – (x + 5)2 = 36. a. y = ±x…

A: Asymptotes are the straight lines which tend to touch the curve at infinity.

Q: Find an equation for the parabola shown in the figure.

A: We have given Vertex: 1, 0 Focus:6, 0   The given graph is symmetric about x-axis. Equation of the…

Q: Find the point(s) on the parabola x =y closest to the point (0,3)

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Q: x ds, where C is the portion of the parabola from (0,0) to (1, 1), followed by the line segment from…

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Q: nd the equation of the parabola with vertex at (5,-2) and focus at (5,-4). (x – 5)² = 8(y + 2) (x +…

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Q: d the x-intercepts of the parabola given by the equation. (If an answer does not exist, enter DNE.)…

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

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Q: Find the focus of the parabola. -x+2x+ 5y-6=0 OD

A: Given query is to find the focus of the parabola.

Q: Which of the following represents a parabola with vertex at (4, -2) and focus at (4, 4)? O A. (x -…

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Q: Determine the standard equation of the parabola opening upward, with focus at (0,6) and whose length…

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Q: Find the point on the parabola x = t, y = t2, -∞ < t < ∞ closest to the point (2, 1/2).

A: Given Data The first equation is x=t. The second equation is y=t². The point is (2,1/2).…

Q: Evaluate x° ds where C is the part of the parabola y = x² from (0,0) to (2, 4).

A: Form the double integral and set the limits than integrate with respect to y and x.

Q: The graph of y^2 = x^3 is called a semicubical parabola. Determine the constant b so that the line y…

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Q: The region in the first quadrant bounded above by the parabola y = x ^ 2 below by the x -axis, and…

A: Follow the steps.

Q: By differentiating implicitly, find the slope of the hyperboloid 22 + y? – 22 = 1 in the x-direction…

A: We have to find slope of the hyperboloid x2+y2-z2=1 in the x-direction at the points (a) 1,2,2 (b)…

Q: The area of the region to the left of the parabola x=2y^2, to the right of the y-axis, and between…

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Q: The a value in the function f(x) = 2x2 makes the parabola %3D O more wider moves it left

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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 parabola with equation y = ax? + bx whose tangent line at (2, 8), is y = -2x + 12.

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Q: 4. What is the focus of the parabola whose equation is -(y- 3)2 = (x – 2)? O A. (2, 1) OB. (0, 3)…

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