Find a line equation through the point P(3,-1,4) and parallel to the line of intersection of the planes 3x-5y+2z%3D1, 2x+y-z=-2. 3+3t A y= -1+7t , - 0

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: Assume the equation of a parabola and a line are given by y = x² + 4x and y=x+4, respectively.…

A: To find out the intersection points of the given parabola and the line.

Q: the Find the distance bebween point of inter Section of the Line %3D X -y -Z =2, 2 x +34 -7Z = -1 |…

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Q: Find all the possible points of intersections of 9x2 + 4y2 + 18x – 16y = 0 and (x + 1)2 + (y– 2)² =…

A: Given curves: 9x2+4y2+18x-16y=0   ········(i)x+12+y-22=5         ········(ii) From equation (ii)…

Q: The equation of the plane that passes through the points (1, -2,1), (-1, -1,7) and (2, -1,3) is :

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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: The lines y where = and y = MON 5x - 7 and y = 2x + 8 intersect at the point (x, y) N

A: To find the intersection of given lines.

Q: Q4-Find the Cartesian equation of the line that passes through the point (-3, 2,-1) and is parallel…

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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: Find an equation of the plane containing the line (x − 3) = −(y + 5) = −(z+2) and the point (5, 0,…

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Q: The line passes through the point (4,4) and is parallel to the line 3x-y=6

A: Given, equation of line and point

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: Write the equation form for the plane defined by co x1 + 1 Ex2 + -10 -0-0-0 + s 3 + t X = x3 = -1 3

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Q: Find the equation of the plane through (1, 0, 1), (−1, 2, 2) and (0, 0, 2).

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Q: Write the equation of the locus of a point whose distance from the plane 3x-2y-6z=12 is always twic…

A: We have to find the locus of the point P with the relation as per the distances given.

Q: A point P(x, y) moves so that the sum of the squares of its distances from points A(0,0)and B(2,-4)…

A: Given,           A point P(x, y) moves so that the sum of the squares of its distances from points…

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.