A circle in the xy-plane has a diameter with endpoints (-1, 3) and (7,3). If the point (0,b) lies on the circle and b >0, what is the value of b ?

Q: In the xy-plane, (-3, 1) and (4, 3) are the endpoints of a diameter of a circle. What are the…

A:

Q: A circle passes through the point (6, 2). If segments of the straight lines x + y = 6 and x + 2y = 4…

A: We can find the radius as below.

Q: A quadrilateral has coordinates R(-5,2),S(-1,3), T(-2,–1) and U(-6,– 2). Verify algebraically, that…

A: Let X be mid point of R(-5,2) and S(-1,3) ∴Coordinate of X is -5-12,2+32…

Q: Calculate the distance from the point (4,−2,7) to the plane x−3y+5z=−8.

A:

Q: A sphere in the first octant is tangent to the three coordinate planes. What is the radius of the…

A: Given:- A sphere in the first octant is tangent to the three coordinate planes To find:- Radius of…

Q: An angle with its vertex at the origin of an xy-coordinate plane and with initial side on the…

A: We know, An angle with its vertex at the origin of an x-y-coordinate plane and with initial side on…

Q: Find the minimum distance from the point (8, 3, 4) to the plane x - y + z = 4. (Hint: To simplify…

A: Let ax+by+cz+d=0 is a plane  Then distance from the  a point (xo,yo,zo) is D= |axo +byo +czo…

Q: Find the distance from the point (3, -4, 2) to thea. xy-plane b. yz-plane c. xz-plane

A: The 3D view of the point is as below

Q: Find the coordinates of the point located in the xy-plane, five units to the right of the xz-plane,…

A:

Q: Find the length of the chord intercepted by the circle x2+y2-x+3y-22=0 on the line y=x-3

A:

Q: Find the points on the cone 2² = x² + y² that are closest to the point (3,-3,0)

A: Cone Equation: z2=x2+y2 Given point: 3,-3,0 To find: the points on the cone nearest to the given…

Q: Calculate the distance between the points P = (-7, 0) and N=(-4, -6) in the coordinate plane. Give…

A:

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: Calculate the distance between the points P = (-7, 2) and M= (1, –1) in the coordinate plane. Give…

A:

Q: 5. Is the point (2, 7) on the circle defined by (x – 2) + (y – 7)2 = 4?

A: Given equation of the circle is: (x-2)2+(y-7)2=4 Given point is: (2,7) Substituting,x=2,y=7 in given…

Q: 4:x=1+21, y =-2+t, z=4-t 1, :x = 5–3s, y= 4- z = 2+

A:

Q: Sketch the second order spline that fits the end points PO (0,0), P2(9,4) and tangents intersection…

A: Here we need to sketch the second order spline that fits the end points P0 0,0, P2 9,4 and tangents…

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: Calculate the distance between the points Q = (-7, 9) and K = (-2, 2) in the coordinate plane. Give…

A:

Q: Find the distance between the points (1, −7) and (4, 2).

A: To find the distance between the given points

Q: A diameter of a circle extends from the point (8,12) to the point(-1,4). What is the length of the…

A: Diameter of the circle is extends from (8,12) to the point (-1,4), then the distance between those…

Q: Find the number of points in the xy-plane with integer coordinates located at a distance 5 from the…

A:

Q: Find the minimum distance from the point (6, 0, 9) to the plane x - y + z = 5. (Hint: To simplify…

A: Given plane is x-y+z=5 and the point is (6,0,9) normal to the plane is (1,-1,1)

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 the distance from the point (4, 3, 0) to the z-axis

A: To determine: Find the distance from the point (4, 3, 0) to the z-axis

Q: Find the coordinates of the point at -50° on a circle of radius 4.7 centered at the origin.

A: x=r cos θ , y=r sin θr is the radius, θ=-50°

Q: Find the radius of a circle with center at (-2,1) if a chord of length 10 bisected at (-3,0).

A:

Q: Find the coordinates of the point located in the xy-plane, four units to the right of the xz-plane,…

A: Let the coordinate of the point located in the xy-plane is x,y,0

Q: A point moves such that the ratio of its distances from two fixed point is constant, show that its…

A: Let the moving point be P (x, y, z). Let A(a, 0, 0) and B(-a, 0, 0) be two fixed points.

Q: Find the minimum distance from the point (6, 0, 5) to the plane x - y + z = 3. (Hint: To simplify…

A:

Q: What is the distance between the point (4,-&, 1) and the plane 5x-z= 2y+5?

A:

Q: The distance from (6,-7, 10) to yZ-plane is

A: Concepts let (x, y, z) be a point then  1) distance of the point from XY plane is…

Q: What is the distance from the point (1,9,3) to the xz-plane?

A:

Q: Find the distance between the points (5,3) and (3,0)

A: Given,          The distance between between the points 5,3 and 3,0.We know that,          The…

Q: A circle centered at (9, 15) has only 1 y-intercept. What is it's radius?

A: Given : Center of Circle is (9 , 15) has only 1 y-intersept. To find : Radius of circle  Solution :…

Q: The circle of radius 1 centered at (-3, 4,1) and lying in a plane parallel to the yz-axis is a)…

A:

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: Calculate the distance between the points M=(-9,8) and L=(-1, 1) in the coordinate plane. Give an…

A:

Q: What is the distance from the point S(-2, 3, -2) to the line of intersection of the planes 2x + 3y +…

A:

Q: The length of the line segment joining the two points of intersection is 3 – x = y = 7+1 With the…

A:

Q: Find the distance from the point (0,8,9) to the plane – 2y + 3z = 11.

A: In this question, we will find the distance from the given point to the given plane.

Q: What is the y-coordinate of all points in the xz-plane?

A: Plane: The y-coordinate of all points in the xz plane , i.e. we need to put y=0.

Q: A circle centered at (9, 15) has only 1 y-intercept. What is it's radius ?

A: we have to find the radius of the circle

Q: Find the distance between the points (p, q) and (0,0)

A:

Q: Find a path that traces the circle in the plane y=5 with radius r=2 and center (-1,5, -4) with…

A: The radius if circle = 2 and center (-1,5,-4) The equation of such circle is given by: The…

Q: Calculate the distance between the points M-(-2,-2) and H-(3,-8) in the coordinate plane. Give an…

A: To find the distance between the points M=(-2,-2) & H=(3,-8). Now, note that the distance…

Q: In the standard (x,y) plane, what is the distance between (3, 4) and (6, 2)?

A:

Q: Which of the fo llowing is a point on the 4) circle whose center is (0,0) and whose radius is 5?

A:

Q: The distance between the line x =-2+2t ,y=2t+1, z=2-t and the line x=3- 2t ,y=-2t+1,z=t is

A: Distance between two Parallel Lines we calculate as a distance between intersection of the lines and…

Q: Find the value(s) of y such that the distance between the points is 6. (-6, 0), (-9, y)

A: Solve for the value of y