Find the equation of the sphere if one of its diameters has endpoints (8, -2, 8) and (11, 4, 17) which has been normalized so that the coefficient of x2 is 1.

Q: Find the equation of the circle passing through the points A(2,1), B(0,5), C(-1,2) using LU…

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Q: At what point does the normal to y = 2 + 2x + 2x² at (1,6) intersect the parabola a second time?

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Q: At what point does the normal to y=4x2−(2+3x)y=4x2−(2+3x) at (1,−1)(1,−1) intersect the parabola a…

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Q: Find parametric equations for the normal line to the surface z=-7x2 -9y2   at the point   (2,1,-37)

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Q: Find the distance from the point (2, –1, 5) to the plane 3x + 2y – 2z – 7 = 0.

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Q: Find an equation of the normal line to the parabola y = x – 9x + 5 that is parallel to the line x -…

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Q: Find the distance from the point (-1, 3, -1) to the plane -1x + 2y -5z=1.

A: Given: The point (-1, 3, -1) and the plane -1x+2y-5z=1 To find: The distance.

Q: Find the general equation of the plane spanned by

A: Given vectors are 111 and 321

Q: Find an equation of the plane determined by the points P(0,0,0), Q(-1,2,4), and R(2,1,3)

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Q: find the distance from the point to the plane. (0, -1, 0), 2x + y + 2z = 4

A: Concept: The two expressions connected by equal to be called an equation. The expression on the two…

Q: 6. For a plane with a normal of ñ = [1,2,-9] and containing a point P (3,-4, 0), write the scalar…

A: Given: Normal of the plane π is given by, n→=i→ + 2j→-9k→ Point P on the plane is P3,-4,0 To find…

Q: Find the distance from the point (-2,0,3) to the plane given by the equation 3x+4y 5.

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Q: By differentiating implicitly, find the slope of the hyperboloid x +y? - z = 1 in the r-direction at…

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Q: find an equation of the plane passing through the three points given.  P = (2, 0, 0), Q = (0, 4, 0),…

A: Equation for plane P is written in vector form as: n.(x,y,z)=d In scalar form equation is written as…

Q: Find an equation of the normal line to the parabola  y = x2 − 4x + 1  that is parallel to the line…

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Q: Find the equation of the sphere if one of its diameters has endpoints (3, -4, 5) and (5, 0, 11)…

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Q: Q1. Find the equation of sphere with center (1, 2,-1) passing through the point (-1, 2, 1).

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Q: Find the distance from the point (3, 4, -1) to the plane lr 3y +2z = 5.

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Q: Find an equation of the normal line to the parabola y = x2 – 8x + 4 that is parallel to the line x –…

A: Let the equation of the normal line in the slope-intercept form is, y=mx+c where m is the slower and…

Q: Find an equation for the set of all points equidistant from the point (0, 0, 2) and the xy-plane.

A: Let any such point is given by (x,y,z)(x,y,z) is z units away from the xy plane.

Q: Eliminate the parameter to obtain an equation in x and y: x=-2cos2t, y=-2sin2t

A: x=-2cos2t y=-2sin2t using trigonometric property,               sin2t+cos2t=1

Q: Find an equation of the sphere with center (2,-3,6) that touches the xy-plane.

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Q: Find the minimum distance from the point (6, 1, 6) to the plane x - y + z = 6. (Hint: To simplify…

A: To find the minimum distance from the point (6,1,6) to plane x - y + z = 6. By using formula,…

Q: Find an equation of the plane passing through P = (1, 2, 3), Q = (0, 0, 3), and R = (−2, 5, 4).

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Q: Find the equation of the normal line to the parabola y = x + 3x – 2, that is also parallel to 7x…

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Q: Find the point on the parabola y = x^2 closest to the point (−3, 0)? and give the minimal distance?

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Q: Find the equation of the sphere which passes through (2, 1, 3), (3, 2, 1), (1, –2, –3), (–1,1, 2).

A: Given that the sphere passes through the points (2,1,3), (3,2,1), (1,-2,-3), (-1,1,2).

Q: Find the equation of the plane that contains the line 2 5-x 2+y – 5 – z, and the 3 point P( 0,5,2).…

A: We have to find the equation of the plane that contains the line and the point.

Q: What is the equation of the normal line to the ellipse 8x^2 + 32y^2 = 256 at the point (4,2)?

A: the equation of the normal line to the ellipse can be found by differentiating the given equation…

Q: Find an equation of the sphere concentric with the sphere x^2 + y^2 + z^2 + 4x + 2y − 6z + 10 = 0…

A: Topic = Geometry

Q: Solve for the linear equation of the plane through the point (1,9,10)(1,9,10) and parallel to the…

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Q: Find the equation of the sphere if one of its diameters has endpoints (3, 1, -5) and (5, 5, 1) which…

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Q: Find the equation of the sphere if one of its diameters has endpoints (7, -2, 8) and (9, 2, 14)…

A: Given: The sphere diameters has endpoints (7,-2,8) and (9,2,14) which has been normalized so that…

Q: Find the distance between the pointx1 =−1, y1 =1, z1 =3 and the point x2 =1, y2 =1, z2 =1.

A: The first point is (-1,1,3) and the second point is (1,1,1) We will use the distance formula:

Q: Find an equation of the plane through the points P(0, 1, 1), Q(1, 0, 1), and R(1, 1, 0).

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Q: Find the points on the cone z = x² + y² that are closest to the point (-5,-2,0)

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Q: Find the equation of the sphere if one of its diameters has endpoints (-5, -5, 1) and (-3, -1, 7)…

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Q: Find the equation of the sphere if one of its diameters has endpoints (-3, -2, -4) and (-1, 2, 2)…

A: Given: The endpoints of one of its diameter are -3,-2,-4 and -1,2,2. The coefficients of x2 is 1.

Q: Find an equation of the normal line to the parabola y = x2 - 8x + 9 that is parallel to the line x -…

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Q: Find an equation for the set of points equidistant from the y-axis and the plane z = 6.

A: we  have to find an  equation for the set of points equidistant from the y-axis and the plane z =…

Q: Find the equation of the plane containing the x-axis and passing through the point (4,3,1/5)

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Q: At what point does the normal to y = 2x2 – (3 + 2x) at (1, –3) intersect the parabola a second time?…

A: Given: y=2x2-3+2x Point: 1,-3 Objective is to find the point where the normal to y=2x2-3+2x at…

Q: Find the point on the circle x2 + y2 = 1 that is closest to the point (1, 3/4) by using the method…

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Q: Find the minimum distance from the point (1, 1, 11) to the paraboloid given by the equation z = x² +…

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Q: Determine the equation of the normal line to the hyperbola x^2 - 4y^2 = 9 at (5,2)

A: We have to find equation of normal

Q: Find an equation of the plane through the three points given: P = (0,0, 2), Q = (-4, 1, –1), R = (2,…

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Q: Determine the equation of the normal line to the hyperbola x2 – 4y2 = 9 at (5, 2).

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Q: Determine the cartesian equation of the plane having x-intercept of 2, a y-intercept of 5 and a…

A: To find the cartesian equation of the plane

Q: Find an equation of the plane through the three points given: P=(0,0,3), Q=(2,−3,2), R=(−1,1,0)

A: find the equation of the plane

Q: Find the equation of the plane that passes through the point P = (1, -5, 2) that has normal n = (-4,…

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