9. Find the standard form of the equation of the parabola with a focus at (-3, 4) and directrix y = 2.

Q: Find the standard equation of the hyperbola. Two corners of auxiliary rectangle at (−4 ,−7) and (0…

A: Given: The two corners of the auxiliary rectangle of a hyperbola are at -4,-7 and 0,0 and transverse…

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

A:

Q: At what point does the line normal to the graph of y=5−4x+4x2 at (1,5) intersect the parabola a…

A: The given function is- y=5-4x+4x2.................1 Differentiating the above expression w.r.t. x-…

Q: 1. Find the equation for the parabola that has its vertex at the origin and has directrix at y = 25…

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Q: Find the equation of the parabola with a focus at (1, -8) and a vertex at (1, - 2). Let a represent…

A: Since the x-coordinates of the vertex and focus are the same, they are one of top of the other. So,…

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 (2, 4) and a directrix of y = 8. 1 O f(x) -(x –…

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

Q: Find an equation of the hyperbola that has foci at (-15, 0) and (15, 0), and asymptotes y= x and y=

A:

Q: Find the standard form equation for a hyperbola with vertices at (6, 0) and (– 6, 0) and asymptote 1…

A: Find the equation of the hyperbola

Q: Determine the DE for: Parabolas with axis to the x- axis and with distance from focus to  vertex…

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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: Find the point on the hyperbola xy = 8 that is closest to the point (3,0)

A: Given: xy=8 so, y=8x now any point of given hyperbola can be written as x,8x so, let's that point on…

Q: State the equation of the parabola which has a focus of (9, 3) and a directrix of y = -3. (Let a be…

A: To find the equation of the parabola having focus and a directrix, let we choose (x, y) be any point…

Q: A] Find the length of the arc of the semi-cubical parabola y² = x3 (1,1) and (5,5V5). between the…

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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 of parabola with rertex at (0,0 and focus at (3

A: Given the vertex is at(0,0) and focus (3, 0)

Q: Find the equation for the parabola that has its vertex at the 1 origin and has directrix at y 41…

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Q: What is the equation of the line tangent to the hyperbola = 1 at the point (V2a, b)? y = -a+b 26 V26…

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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: 1 Find the equation for the parabola that has its vertex at the origin and has directrix at y 27…

A: Given: y=-127.

Q: Find the minimum distance from the point (4,2) to the parabola y2 = 8x.

A: We have to find the minimum distance from the point (4,2) to the parabola y2=8x.

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

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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

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Q: Find an equation of the hyperbola that has foci at (-10,0) and (10,0) , and asymptotes y=3x and…

A:

Q: The parabola y = x² is shifted up by 4 unit %3D What is the equation of the new parabola?

A: Parabola:y=x2  shifted up by 4 units

Q: 8. Find the equation of the parabola with vertex at (0, 5) and passing through the point (4,3)…

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Q: Find the standard form of the equation of the hyperbola satisfying the given conditions: Endpoints…

A: Since, endpoints of trnsverse axis lie on y-axis,so transverse axis of hyperbola is y-axis, so the…

Q: If tangent lines to the hyperbola 9x2 − y2 = 36 intersect the y-axis at the point (0, 6), find the…

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Q: Find the standard form of the equation of the hyperbola satisfying the given conditions as End point…

A: Find the standard form of the equation of the hyperbola satisfying the given conditions as End point…

Q: Which is the corresponding equation of the hyperbola with foci located at (-8, 0) and (8, 0) and a…

A:

Q: Find the standard form of the equation of the parabola with the given characteristic and vertex at…

A: equation of parabola  (x - h)2 = 4p (y - k) where (h,k)=(0,0) vertex ordinates directrix y=3 , y= k…

Q: Find a Cartesian equation for the hyperbola centered at the origin that has a focus at (3, 0) and…

A: The focus is 3,0 c,0=3,0∴c=3 Also the directrix x=ae=1                           ∴a=e Now…

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

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Q: Find the equations of the normal and the tangent to the hyperbola xy + 2x - 5y-2= 0 at the point (3,…

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Q: Find the equation of the hyperbola that is centered at (0,0), has vertices at (t10,0) and has 6.…

A: Consider the given values. Center=0,0vertices=±10,0y=±65x The gerneral equation of hyperbola with…

Q: 1 in (r', y')-coordinates, if (iii) Find the equation for the hyperbola ry 0 = 1-

A: Find the equation of hyperbola in x'y' system

Q: Picture of question is attached.

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Q: 9. Find equations for two lines through the origin that are tangent to the ellipse 1² – 4x + 4y² =…

A: We have to find

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

A:

Q: 1. Find the point on the parabola y = 3 – x² that is closest to the point (6, 0).

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Q: 1 Find an equation of the hyperbola having foci at (5-/45, 0) and (5+/45, 0) and asymptotes at y = 5…

A:

Q: Which is the corresponding equation of the hyperbola with foci located at (−8, 0) and (8, 0) and a…

A: Given data is : Foci are -8,0 and 8,0 The transverse axis is 14 unit

Q: Find the equation for the parabola that has its vertex at the origin and has directrix atI = 27…

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Q: Find an equation of the hyperbola that has foci at (-10, 0) and (10, 0), and asymptotes y = 7x and…

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

A:

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.