Find the point(s) on x = 3 - y that are closest to point A = (1,0).

Q: Find the point on the ellipse x = 2 cos t, y = sin t, 0 ≤ t ≤ 2π, closest to the point (3/4, 0).…

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Q: Find the coordinates of the point(s) on the curve y = Va + 3 that are closest to the point (8, 0). O…

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Q: A heat-seeking particle is located at the point (2, −3) on a metal plate whose temperature at (x, y)…

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Q: Find the distance from point P(1,1,1) to the pl r +y +z = 1

A: We have to solve

Q: Find the points on the curve x2 + xy + y2 = 16 which are nearest and farthest from the origin.

A: Given curve is g: x2+xy+y2=16 If x,y is any point on the curve g: x2+xy+y2=16 Then square of the…

Q: 2. Find the equation of the plane tangent to the elliptic paraboloid z = point (1, 1,3). 2.a2 +y, at…

A: To find out the equation of the plane tangent to the elliptic paraboloid.

Q: Determine the location of a point (x, y, z) that satisfies the condition y < 0

A: With the given condition there are 4 scenarios 1) x>0,y<0,z>0 2) x<0,y<0,z<0 3)…

Q: Find the point on the Curve y rx that is closest to the point (2,0)

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Q: Integrate ƒ(x, y, z) = x - 3y2 + z over the line segment C joining the origin to the point (1, 1, 1)

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Q: ) Find the orthogonal trajectories of the family of curves r = 3C sin 0, where C being parameter.

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Q: 8. Determine the equation of the plane tangent to z point (x, у, z) 3 (-2, 1, 4). x*y3 at the =

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Q: b) Find the point on the curve y Vr that is closest to the point (7,0).

A: Find the point to the curve y=(x)^(1/2) that is closest to the point (7,0)

Q: Find the tangent plane to the equation z = 2x – 3y + y at the point (1, 2, – 8). -

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Q: Find the point on the ellipse x = 2 cos t, y = sin t, 0 <=t<= 2pai closest to the point (3/4,…

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Q: 9. Find the point (x, y) on the line y = 2x + 3 such that the distance from (x, y) to (1, 1) is as…

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Q: Find equations for the lines tangent and normal to the cissoid of Diocles y (4 – x) = 9x° at (2,6).

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Q: Find an equation for the tangent plane to z-x-y = 3 at the point (2, 1, 8) Z - ) %3D

A: given z-x2-y2=3 at point 2,1,8

Q: Find the shortest distance from the point P(2,-1, 1) to the plane with =quation x - y + 2z = –1 and…

A: Shortest point of the given plane and point P.  Distance from the point P and Q

Q: Find the equation of the plane tangent to the graph of z + xyz = 33 at (1,2,3).

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Q: Find the tangent plane to the equation z = 3e²²-2y at the point (4, 8, 3)

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Q: Find an equation of the parabola y = ax2 + bx + c that passes through (0, 1) and is tangent to the…

A: Given" Parabola y = ax2 + bx + c that passes through (0, 1) and is tangent to the line y = x − 1 at…

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

A: Concept -Let the equation of plane be -Ax+By+Cz+D = 0And the coordinates of a point be - (x1, y1,…

Q: Find the length of the curve y = 1 - e^-x, 0 <=x<=1.

A: The given curve is

Q: Find the tangent plane to the equation z 5a2 - 4y +5y at the point (5, 5, - 200)

A: The equation of the tangent plane to a surface  is given by fx(x-a)+fy(y-b)+fz(z-c)=0where (a,b,c) =…

Q: 2. Find the point on the curve y = VI thats is closest to the point (3,0)

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Q: Determine the coefficients a, b, c and d so that the curve y = ax* + bx³ + cx² + dx + e will pass…

A: Since we have to find value of a,b,c and d

Q: Find the equation of the plane tangent Z = (x+2)*- (y-1)²-5 at (2,3,3) to

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Q: Find the tangent plane to the equation z 5z° + 4y – y at the point (4, 2, – 66)

A: Given: z=-5x2+4y2-y      4,2,-66

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: The line that is normal to the curve x + 2xy - 3y = 0 at (4,4) intersects the curve at what other…

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Q: 2-g(%,y)%3D플-플 * at (VT ,1)

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

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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 the distance between the point (3,11,-2) and the plane X t 2y

A: Explanation of the answer is as follows

Q: Determine the location of a point (x, y, z) that satisfies the condition xyz > 0

A: In four of the eight octants xyz>0 1) x>0, y<0, z<0 (2) x<0, y>0, z<0 (3)…

Q: Find the tangent plane to the equation z 4e- 4y at the point (8, 16, 4)

A: Let x0,y0,z0=8,16,4 be a point on the given surface. Then, the equation of tangent is…

Q: Find the length of the curve. y = In(secx), 0Sx</4

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Q: Find the equation of the tangent plane to the surface -2² at the point y = 2x2 – (0, –1,2)

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Q: Find the length of the curve y Inx at (2<x< 4)?

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Q: Find the distance between the point (1,1) and (3,9) along the curve y=x2

A: Given:The points (1,1) and (3,9) along the curve y=x2To find the distance we need use calculus as…

Q: (A) Find the unique point P on the y-axis which is on both planes. (–, ,

A: As per our guidelines we are supposed to answer only one question. Kindly repost other question as…

Q: Find the family of oblique trajectories that intersect the family of the paraboles y =cx at angle 0…

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Q: Find an equation of the parabola y = ax² + bx + c that passes through (0, 1) and is tangent to the…

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Q: Find the distance from the point (3, -4, 2) to the xy-plane

A: Given: 3,-4,2

Q: find the location of a point xyz that satisfies the condition I) xy<0, z=3 ii) |x|<2

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Q: integrate ƒ over the given curve. ƒ(x, y) = x2 - y, C: x2 + y2 = 4 in the first quadrant from (0, 2)…

A: The given curve C is a circle with center at origin and radius of 2 units. Let the parametric…

Q: Find the equation of the tangent plane to the surface y = 2x² – z² at the point (0,-1, 1)

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Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.