Give the equation of the parabola with focus F (0; 2)  and directrix y = -2 . Give an equation of the parabola that can be obtained from the previous one via translation and its axial point is (3; -1) .

Q: Use the Distance Formula to show that the equation of the parabola with focus F(0, 1) and directrix…

A: Given that Focus of parabola is F0, 1. Directrix is y=-1. We have to prove that y=14x2 is the…

Q: Give the standard equation of the parabola with focus (-3,0) and directrix x=3

A: Standard equation of parabola is y2=±4ax Given that focus of parabola is (-3,0) and directrix is…

Q: Find the equation of the parabola with vertex at the origin and satisfies the condition: Focus…

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Q: Find the standard form of the equation of th parabola with: and Focus (-2, 6) Directrix X = 8

A:

Q: What is the equation for the parabola below in terms of its focus and directrix? y = _____

A: Given: equation of the parabola

Q: Find the standard equation of the parabola which satisfies the given condition. Focus (7, 11),…

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Q: Find the equation of the parabola with focus (-3, 0) and directrix x-3.

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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: Use the Distance Formula to show that the equation of the parabola with focus F(0, 2) and directrix…

A: Given:            Focus of parabola is : F(0,2)Directrix is:​y=−2.

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

A: Given: Opens downward with focus 10 units away from the vertex.

Q: Find an equation for the parabola with focus (0, -4) and directrix y =

A:

Q: Find the equation of the parabola with focus at (5, 0) and directrix x = −5.

A: Focus lies on x-axis.

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

A:

Q: 9. Find the standard form of the equation of the parabola with a focus at (-3, 4) and directrix y =…

A: the vertex of the parabola will be at the midpoint of (-3,4) and y=2  That is Vertex= (h,k)=(-3,3)…

Q: Find the equation for the parabola that has its vertex at the origin and the focal point is 278…

A: Consider the equation of parabola vertex at origin and focus to the right of directrix. y2=4ax…

Q: What is the equation of parabola in standard form with focus F(- 2, – 1) and directrix y=3? A(y-1)2…

A:

Q: Derive the equation of the parabola with a focus at (6, 2) and a directrix of y = 1. 1 O f(x) = -- 2…

A: We can derive the equation of parabola as below.

Q: Find the standard form of the equation of the parabola satisfying the given conditions: Focus :…

A:

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: Find the standard form of the equation of the parabola satisfying the given conditions: Focus :…

A:

Q: Find the standard form of the equation of the parabola satisfying the given conditions: Focus :…

A: To find the equation of the standard form of parabola Focus -10,0 Directrix x=10

Q: Determine the equation of the parabola using the given information. Focus (0, −3) and directix y =…

A:

Q: Find an equation of the parabola that satisfies the given conditions.Focus F(2, 0), directrix x = -2

A: If the coordiantes of the focus h+p,k and directrix x=h-p Then, equation of parabola y-k2=4px-h We…

Q: Find the standard form of the equation of the parabola satisfying the given conditions: Focus : (0,…

A: given, focus (0,15) directrix y=-15

Q: Determine the equation of the parabola given the focus at (-10,23/2) and directrix at y=-11/2.

A: Given- Focus -10,232 and directrix y=-112 To Find- The equation of the parabola.

Q: 2. Find the equation of the parabola described. a. Vertex at (4, –2); focus at (6,–2) b. Focus at…

A:

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 an equation of the hyperbola that has foci at (-2, 0) and (2, 0), and asymptotes y = x and…

A: The hyperbola has foci at -2,0 and 2,0 and asymptotes y=x and y=-x

Q: Use the Distance Formula to show that the equation of the parabola with focus F(0, 1) and directrix…

A: Given that Focus of the parabola is F0, 1 and Directrix is y=-1 We have to prove that y=14x2 is the…

Q: Find the standard equation of the hyperbola with the stated conditions. Vertices at (2,-5) and…

A:

Q: 24. Construct the equation of a parabola with focus at (-1,2) and a directrix x = -7.

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Q: Find the standard form of the equation of the parabola. Focus at (0, 4), directrix y = -4

A:

Q: Find an equation of the parabola in standard form with focus at (3,0) and directrix x=-3

A:

Q: Find the equation of the parabola with focus (1, −4) and directrix y = 0.

A: Given the following to find the equation of parabola.

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: 21 Find the equation for the parabola that has its focus at the 2 and has 4 11 directrix at æ = 4…

A:

Q: Find the standard form of the equation of the parabola satisfying the given conditions: Focus : (0,…

A: Given:Focus0,20Directix y=-20Parabola:x-h2=4p y-k

Q: Find the standard form of the equation of the parabola satisfying the given conditions: Focus : (7,…

A: Parabola: The focus of the parabola is (7,1) Directrix of the parabola is y=-9. The equation of…

Q: Find the standard equation of the parabola which satisfies the given conditions. Focus (-2, -5),…

A:

Q: which satisfies th

A: Parabola: The focus of the parabola is (-2,-5) The directrix x=6 The general form of parabola is…

Q: Find the equation of a parabola whose focus is at(2,-3) and directrix's equation is x=5.

A: Distance between the point x1 , y1 and a lineax+by+C=0 is ax1+by1+Ca2+b2

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

A:

Q: find the orthogonal trajectory of family of parabolas represented by the equation…

A: To find orthogonal trajectories of  y2=4ax.

Q: Find the standard form of the equation of the parabola satisfying the given conditions: Focus : (2,…

A: Consider trhe focus of the parabola is 2,4 and the directrix is x=-4. Let x,y be any point on the…

Q: Which is the equation of a parabola with a directrix at y = 2 and a focus at (5, 0).

A:

Q: Find an equation of the parabola that satisfies the given conditions.Focus F(0, -4), directrix y = 4

A: To find: The equation of the parabola that satisfies the given conditions. Given information: Focus…

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.