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: Write the equation of a circle with centre (5, –2) which is tangent to the Y-axis. o (x + 5)² + (y –…

A: Here we have to write the equation of a circle with centre (5,-2) which is tangent to the y-axis.

Q: - Show that the equation of the circle passing through (1, 1) and the points of intersection of the…

A: we need to show that equation of circle passing through (1,1) and point of intersection of given two…

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

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Q: 4. Which line is the horizontal asymptote for the hyperbola y = 6/ ( x - 5 ) + 9 y = 9 X = 5 y= -6/5

A: given,     the parabola y=6x-5+9

Q: Find an equation of the Hyperbola that has Foci (-1,–3) & (-1, 7) with asymptotes y = x+ & y = -a+…

A: Standerd equation of hyperboal is (x-h)2a2-(y-k)2b2=1where (h,k ) be the center

Q: 5) Find the vertex and axis of symmetry of the parabola with focus F(7/2,3) and directrix line…

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

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Q: The vertex of the parabola with focus (-2,-4) and directrix y - 4 is o (1,-4) 0 (-2,1) O (0,-4) O…

A: Given,drectrix of parabola is y=4,And focus is at (-2,-4)It is clear that parabola is open down,and…

Q: Find the equation of a sphere whose center is on line 5y+2z=0=2x-3y and passes through point…

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Q: Which of the following properties satisfy the parabola with equation x² + 6x + 8y = 7 O v(3,2);…

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Q: Find an equation for the sphere with center at (-7,8,0) and radius = 9 O x2 + y? O x2 + y2 + z- -…

A: We have to find

Q: = 8. Find the equations of both the tangent lines to the hyperbola x² - 4y² 9 that pass through the…

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Q: Find the equation of the sphere of radius 8 centered at (1, 3, 6). O x² + y² +z² = 46 O x² + y² + z²…

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Q: Find the equation of a circle in standard form whose center is at (-4,3) and radius v5 * O…

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Q: Find the equations of the osculating circles of the parabola y = 3(x – 2)2 at the points (2,0)

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Q: The orthogonal trajectory of y = ce* is a parabola of the form y = ax+b. Find the values of a & b so…

A: We are asked to find the value of a and b

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: 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.