Determine an equation of the line passing through the points A(4, −2, 3) and B(5, 1, 2). Determine the point(s) at which the line from problem 3 intersects the sphere x² + y² + z² = 30 How far away is the point P(2, 1, 2) from the line in problem 3?

Q: The parabola y = ² is changed to the form y = a (x − p)² + g by translating the parabola 2 units…

A: The parabola y=x2 is changed to the form y=ax-p2+q by translating the parabola 2 units down and 3…

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

A:

Q: Find the equation of the sphere having the circle x +y+ z2 = 9, x- 2y+ 2z = 5 as a great circle.

A: The solution is below.

Q: 5) Find the unique quadratic curve (i.e. parabola) which passes through the following three points:…

A: We have to find the unique quadratic curve which passes through the following points:…

Q: What is the equation of the parabola containing the points (0, 5), (–1,9), and (2, 3)? O y = r-z+5 O…

A: The standard form of a parabola is y=ax2+bx+c. The required parabola passes through the 3 points are…

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: Find the equation of the line passing through the point (7, 2) and perpendicular to the line 5y = 9…

A:

Q: find the equation of a sphere with the line segment AB as one of its diameters, where A(-3, 2, 1)…

A: We have to find the equation of a sphere with the line segment AB as one of its diameters, where…

Q: 2. Write the symmetric equation of a line through the points (0, 2,8) and (3,-3, 4). Find where this…

A:

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

A:

Q: Find the x² + y² − 3x − 6y + 14 = 0, - equation of the circle which cuts th x² + y² − x − 4y + 8 = 0…

A: The circle having center at the radical center of the three given circles and radius equal to the…

Q: (3) Find the coordinates of the points of intersection of the parabola y = x2 - ax and the line y =…

A:

Q: 1. The three points A = (-2, -4), B= (6,2) and C = (-3,3) are taken as the vertices of a triangle T.…

A: Given that: A=(-2, -4), B=(6, 2), C=(-3, 3)

Q: Determines the Cartesian equation of the plan that is parallel to the plan 2x - 3y + z - 1=0 and…

A: We have to find the equation that is parallel to the plane 2x-3y+z-1=0. Also plane passes through…

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

A:

Q: O y = -(x+ 4)² + 5 | O y = -(x- 4)² – 5 | O y = #(x – 4)² + 5 O y = -( - 4)² + 5

A:

Q: To y=x²-12x + 20 Parabola Wite the intersection point of the tanpent lines drawn from (2,0) and…

A: Consider the given parabola and find the derivative of the parabola.…

Q: A square has an area of 36 and one side that lies along the line y = 3. What could be the location…

A: To find the possible co-ordinates of square.

Q: A point moves so that the ratio of its distances from 3x + 4y + 8 = 0 and 4x + 3y – 6 = 0 is 2. Find…

A:

Q: Compute the surface integral over the given oriented surface: F = (0, 0, e³+²), boundary of the cube…

A:

Q: The equation of the sphere with Center (4,-1,3) and radius √5 is

A:

Q: the point (8,-5) is 6 units above the point P(x,y) and 3 units to the right of it, then what are the…

A: