9 2x – 5xy + 2y?

Q: Q 03: find the orthogonal trajectory of family of parabolas represented by the equation y? = 4ax…

A: Given y2 = 4ax2y dydx = 4adydx = 4a2ya = 2yy'4= yy'2y2 = 2xy dydx

Q: Discuss and trace the curve of the following equation. 2. y = x+3 у %3D 1. у %3D x²-16

A: The general form of a polynomial function is given by a0xn+a1xn-1+···+an, where a0, a1,···,an are…

Q: Suppose a golf ball is driven so that it travels a distance of 200 feet as measured along the ground…

A:

Q: Find the equation of the parabola, y = ax^2 + bx + c, that passes through the points (0,5), (2,-5),…

A: we have to find the equation of the parabola y=ax2+bx+c that passes through the points (0,5), (2,-5)…

Q: An ellipse has the equation 16x² + 25y = 40O. Determine the equation of the tangent of the curve at…

A:

Q: Some comets, such as Halley's comet, are a permanent part of the solar system, traveling in…

A: Let the equation of hyperbola  be x2a2-y2b2=1 Since the asymptote are perpendicular, so a=b By the…

Q: Consider the equation x2 + 8x² + z² = 30, then take a cross section when x = 1. Describe the…

A: 6.     Resulting shape gives two parallel line.

Q: By applying derivatives, which among the following equations of parabola would yield to a vertex of…

A: Given The given vertex is V=12,-812. For vertex of the parabola, Find the slope of the quadratic…

Q: In Problem,identify the graph of each equation without applying a rotation of axes.

A: Given : The equation is 10 x2 + 12 x y + 4y2 - x - y + 10 = 0 .

Q: 9. Find b and c so that the parabola y = -3x? + bx + c has intercepts 1 and – 4.

A:

Q: A parabola is defined by the equation y=x2+2x+3. Write equations of the tangents to the parabola…

A: Given the equation of parabola:

Q: Hx'+y°-4x+Dy = - 2

A: This question is based on formation of perfect square and solving inequality notation.

Q: 2. Sketch and identify the graph of the equation a + y? – 2y –- 3 = 0 in 3D.

A: x2+y2-2y-3=0x2+y2-2y+1-4=0x2+(y-1)2=4The equation represents circle in 2D,but a cylinder of radius 2…

Q: Find an equation for the indicated half of the parabola.Lower half of (y + 1)2 = x + 3

A: Given equation is y+12=x+3.

Q: The equation of a parabola is y = -x 2 -4x + 3 . Give the equation of the axis of symmetry of the…

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Q: Which is an equation of the parabola shown in the accompanying diagram? 1 -21 y = -x² + 2x + 3 A. y…

A: We will find the factors of this function using the roots. The roots of the function are those…

Q: Which point or points on the ellipse x? +4y? = 4 are furthest away from the point (0, 1)?

A: The Equation of the given ellipse is, x2+4y2=4 Let the furthest away point on the ellipse, from the…

Q: In Problem,identify the graph of each equation without applying a rotation of axes.

A: The given equation is 2x2-3xy+4y2+2x+3y-5=0. Sketch the graph of the above equation as shown below.…

Q: In Problem,rotate the axes so that the new equation contains no xy-term.Analyze and graph the new…

A: Given: 9x2-24xy+16y2+80x+60y=0

Q: A parabola is given by the equation y = x^2 - 4x + 6. Find k so the line of equation y = 2x - k does…

A: We have to find the value of k for which the line intersect the parabola at two distinct points. To…

Q: 2. Sketch and identify the graph of the equation a+y? - 2y-3 0 in 3D.

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Q: Suppose a golf ball is driven so that it travels a distance of 400 feet as measured along the ground…

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Q: Determine the point on the hyperbola –10r2 + 2y? = 10 closest to the point (-6, 0). 20 15 10 5 -5…

A: Here we have to determine the point on the hyperbola -10x2+2y2=10 closest to the point (-6,0) .

Q: Suppose a golf ball is driven so that it travels a distance of 200 feet as measured along the ground…

A: The given data is: Suppose a golf ball is driven so that it travels a distance of 200 feet as…

Q: Consider the following equation. y = x2 + 5x − 2 (a) State whether the axis of symmetry is a…

A: Given, equation is

Q: Find the equation of the parabola y = ax? + bx + c passing through the points (0, 6), (- 2, 2), and…

A:

Q: Determine the two equations necessary to graph the hyperbola with a graphing calculator. y? - 64x? =…

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Q: -10 10 -6 y? = 1. 62 Identify a and b for the hyperbola with equation - a = b = 6 3.

A: Given, The graph of the  hyperbola  The equation of the hyperbola is x2a2-y2b2=1  We have to find…

Q: In Problem,identify the graph of each equation without applying a rotation of axes.

A: The given equation is 10x2-12xy+4y2-x-y-10=0. Compare the above equation with its standard form…

Q: In a simple video game, a rocket travels in an elliptical orbit whose path is described by the…

A: Given, Equation of the ellipse 4x2 + 25y2 = 100 Now, rocket is travelling to the tangent to its path…

Q: In Problem,identify the graph of each equation without applying a rotation of axes.

A: The general equation of conic section is given as Ax2+Bxy+Cy2+Dx+Ey+F=0 . Its discriminant is equal…

Q: -9 a = -6 b = 3 6 4 2 -2 -4 -6 Identify a and b for the hyperbola with equation e x² a² 62 = 1.

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Q: Find an equation for the indicated half of the parabola.Right half of (x + 1)2 = y - 4

A: (x+1)2=y-4

Q: The equation x2 + y? + 2x-4y- 10 0 represents: %3D | circle O point O has no graph O

A:

Q: 5. Put the following equation into standard form, classify it as a circle, ellipse, hyperbola, or…

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Q: Find an equation of the parabola that has focus F (-3,-3) and directrix y = 1

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Q: 2. Put the equation in standard form then sketch a graph indicating the foci and end points: 9x2 +…

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Q: Find the intersection point(s) of the curves whose equations are: 5x - 4 %3D 2x - 4x + 22 The…

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Q: A circle is graphed in the xy-plane. If the circle has a radius of 3 and the center of the circle is…

A:

Q: What are the apparent roots of the equation graphed on the coordinate gid? -5 "5 4 3 2 101 2 3 45 -3…

A: The roots of the equation are the x-intercepts of the graph.  In the given graph, the x-intercepts…

Q: Find all the values of b such that the parabola y=(1)/(8)x^(2)-bx+(9)/(2) will have a directrix…

A: the given equation of the parabola is y=18x2-bx+92. we have to find all the values of b so that the…

Q: Find an equation of the parabola that satisfies the given conditions.Focus F(-3, -2), directrix y =…

A: We have given the equation of directrix is y=1 which parallel to the x-axis. The standard equation…

Q: Which of the following equations is the equation of tangent to the parabola y = 2x +8 at (4,4) ? (a)…

A: Given equation of parabola is Differentiating both sides with respect to x, we get Slope of…

Q: F(0,0)D:x=4  Find an equation of the parabola described.

A: Given focus=(0,0) Directrix: x=4  So the vertex is at the mid point of (0,0) and x=4 That is…

Q: Find all values of b such that the parabola y = x² – bx + will have a directrix having an equation…

A: y=18x2-bx+92 On simplification, we get…

Q: 1) Find the intercept(s) and vert ex of the parabola. y=x^2-1

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Q: 12. Determine the equation of the directrix for the parabola 20x=y2–10y+30 а. X-20 b. y=-20 с. X3-20…

A: Question : Determine the equation of the directrix for the parabola 20x = y^2 - 10y +30.

Q: Find a, b, and c so that the graph of the parabola with equation y=a+bx+cx^2 passes through the…

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Q: Which of the following equations is the equation of tangent to the parabola y = 2x + 8 at (4,4)? (a)…

A:

Vertices Of An Ellipse

In the study of the conic section of the geometry, An ellipse is a plane curve surrounding two focal points, or foci where the set of all locus of points in the plane has their sum of the distances to the two foci is constant. On the ellipse curve, it is the intersection point of the main axis. In an ellipse graph, the center of the axis is the midpoint of the line segment connecting the foci. The major axis is the line section that runs through the ellipse's foci, while the minor axis runs through the middle and is perpendicular to the major axis.. The ellipse has two endpoints on the major axis which are known as the vertices (in plural), vertex in the singular. The equation of the major axis is 2a, the equation of the minor is 2b and the distance between the major axis and minor axis is 2c. The semi-major axis has a length of a and the semi-minor axis has a length of b. The ellipse's vertices are determined by the elliptical orbit's equation and graph.