Find the standard form for the hyperplane through the point (1,0, -2, 1) with normal (1, 1,2,-1). A x₁ + x₂ + 2xy - x₁=0 OB. x₁ + x₂ + 2xy-x₁=-4 OC. x₁-2x3+x=0 OD. x₁-2xy + x₁=-4 OE. x₁ + x₂ + 2x₁-x=7 Reset Selection

Q: a point Q(x2, y2) is on the line segment passing through R(-2,5) and S(4,1). Find the coordinates of…

A: Given: Given that the point Qx,y is on the line segment passing through R-2,5 and S4,1 Point Q is…

Q: circle passes through the points (2,1) and (-2,3) and its center is on the line 2x＋y＋4=0. Find its…

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Q: 2. Consider the parabola whose equation is (x + 5)2 = -16(y – 7). What are the coordinates of the…

A: “Since you have posted a question with multiple sub-parts, we will solve the first three sub-parts…

Q: 3. Find the vertex for the parabola 4x + 2y² + 8 = 0. (a) (0, -2) (b) (-2,0) (c) (2, 2) (d) (-2,1)

A: The equation of the parabola is  4x+2y2+8=0

Q: 13. Which of the following is the equation of the graph shown? 2 Parabola Oy = - 3x? – 6x – 2 Oy = -…

A: The objective is to find the equation of the graph.

Q: What is the center of the sphere given by the equation x² − 6x + y² – 2y + z² + 8z + 17 = 0? -…

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Q: Q3/ Find the equation of the plane that contains the line 3-x 2+y %3D 3 - z, and the point P (1, 4,…

A: Given line is  3-x4=2+y2=3-zand the point is (1,4,3) find the equation of the plane

Q: 7. A parabola whose equation is y =r² - 2x + k has a turning point with coordinates (1,-5). Find the…

A: We have to find k

Q: write the equation of the quadraticfunction whose graph is a parabola containing the givenpoints

A: Let the equation of the quadratic function be: fx=y=ax2+bx+c This function passes through the points…

Q: 1. Find an equation of the perpendicular bisector of the segment joining(3. -1) and (-1. 7). (A) x +…

A: Here we have to find the equation of line which is perpendicular bisector of the segment joining(3.…

Q: Determine the x-intercepts of the following equation. (-x+ 5)(-a - 2) = y | O (5,0) and (-2,0) O…

A: The objective is to determine x - intercepts of -x+5-x-2=y       ...... (1) To find x - intercepts,…

Q: XIV. Give equation of straight line through point (1,3,-2) perpendicular to z = Зх-2y +4.

A: Given z=3x−2y+4 and point is x0,y0,z0=1,3,−2 We have to find the equation of straight line through…

Q: At what point does the graph of 3x+y=0 and x-y=D4 intersect?

A: Given: 3x+y = 0 y = -3x And x-y = 4 y = x-4

Q: Standardize the conic with the equation 7x2+4xy+4y2--2x-6y+1=0

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Q: Determine the point on the graph of z = x² + y²+ 10 closer to the plane x + 2y-z = 0

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Q: A die is rolled 11 times. Find the probability of rolling the following.   Exactly 11 threes. The…

A: A die is rolled 11 times means 1 die is rolled 11 times. The possible outcome in single die…

Q: If a parabola y=ax2+ky=ax2+k has vertex (0,−1)(0,−1) and passes through the point (4,2)(4,2). What…

A: A Parabola y=ax2+k       ...(1) has Vertex (0,-1) and Passes through the Point (4,2)

Q: Find the directrix of the parabola described by the equation 6 (x – 3) + (y + 2)? = 0 O x = } O x =…

A: The  parabola with vertex at (h,k) and focus at (h-a,k) has a standard equation, (y-k)2=-4a(x-h) The…

Q: The vertices of the ellipse given by = 1 are (2, 1) and (1, 2) (0, 1) and (0, – 1) - O A. В. (-2, 0)…

A: Given:- x2/4+y2/1 = 1 To find:- Vertices of given equation of ellipse

Q: Write the equation of the hyperbola 9z²- form Where: h = 4 k= 1 a-9 b= -72 (z-h)² a² S q X X X…

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Q: est to the point 2, 2

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Q: Find the equation of sphere that passes through the point (-2, -8, -2) and centered at (8, 7, 8).…

A: To find the equation of the sphere that passes through the point -2, -8, -2 and centered at 8, 7, 8.

Q: Let X = [a, b, c]. Let U be the subspace spanned by the orthogonal basis {u = [1, 1, 1], v = [1, -1,…

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Q: What are the intersection points of the parabola given by the equation y = x2 – 9 and the line given…

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Q: Find the equation of the parabola y = ao + a₁ + a2x² that passes through the points (-1 -9), (0,…

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Q: 5. 3. 2. 518 2. 6. 3 2. 9. 3. 5. 3. 2.

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Q: Find the equation of the parabola with the following data. F (-3, -2), V (-3, -5)

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