A circle with radius 2 contains the point (1,-4). Which of the following equations best describes the possible coordinates of the center (h,k)? O h- -4k O (h-1) = 2(k+4) O (h, k) = (1. -4) O (h-1) + (k+4) = 4

Q: An ant is walking on the xy-plane is such a way that its distance to the point (2, 4) is always the…

A: Solution: Let the point P(x,y) is the position of Ant and given that the distance from P(x,y) to…

Q: Give the general equation of the plane containing the point (3,-1,4) and perpendicular to the line =…

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

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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: Find the point on the line 5x + y = 5 that is closest to the point  (−4, 1).   x,y= (  , )

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Q: What is the equation of a circle that has center located at (- 2, 0) and passes through the point…

A: Solution: The objective is to find the equation of a circle that has a centre located at (- 2, 0)…

Q: Two cars are traveling on two different roads that are perpendicular to each other. On a coordinate…

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Q: What is the image of the point (2,-3) after the transformationr y-axis 1) (2,3) 2) (-2,-3) 3) (-2,3)…

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Q: Find the equation of the line through point (2, 1/2, -3) and is perpendicular to the plane -x+4y+3z…

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Q: Find the distance between the points A = (2, 0, (2, 0, 1) and B = (4, 5,-2)-

A: Given that two points   A =2, 0, -1     and   B = 4, 5, -2      If two points were given, then…

Q: Find the point on y – axis which is equidistant from the points (3, 1, 2) and (5, 5, 2)

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Q: :Find the equation of the plane through (-1 6, 2) and perpendi cular to the jain of (1, 2, 3) and…

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Q: The surface described by the equation 3x-+3y-+3z--8x+4z+38=0 is

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Q: Two planes with equations x - y + 2z=4 and x + 2y - z = -5 intersect along a line L. Determine the…

A: Find the intersecting line L. For any random point on the line L, we can find the general distance.…

Q: Find the coordinates of the image of the point (-22) when it is reflected across the line y-7 O…

A: Given that the line y=7 and the coordinates whose image has to be found is (-2,2) Let A be the…

Q: Find the exact value of the distance between the line of intersection of the planes 2x-y+2z 6,…

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Q: Find the equation of the line through point (3,7,-11) y is perpendicular to the xz-plane

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Q: Find an equation of the plane that passes through the point (1, 6, −4) and contains the line:

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Q: Find an equation of the plane pirpendicular to the line through (2,2,-4) and (9, "1, 3) and…

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Q: Find the coordinates of the point 7. of the way from A to B. 10 本y 10 8- B(t0,7) 6- 2- -> -6-4-2 -2…

A: Given P is a point 710 of the way from A to B .This implies that point P divides the line AB in…

Q: tangent to the parabola y=x^2

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Q: What is the equation of a circle with its center at (0,–2) and passing through the point (3, –5)?

A: Given,          The equation of a circle with its center at 0,-2 and passing through the…

Q: 11) The distance from the point S(7, 6, -8) to the line x = −2 + 4t, y = -9 + 3t, z = 3 + 12t 12)…

A: #11) Given: Point = S7, 6, -8 and the line x=-2+4t, y=-9+3t, z=3+12t. To find: We have to find the…

Q: (a) The curve with equation 2 y 3 + y2 - y 5   = x 4 -2x3  +x 2  has been likened to a bouncing…

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

A: We have to find the distance from the point 3,-4,2 to the yz-plane. We know that if any point px,y,z…

Q: 2. Find an equation of the sphere that passes through the point (2, 3, –1) and has center (-3, –1, –…

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Q: The drone starts at point (0, 0), the landing pad is at point (11, 3) and the parabolic path must…

A: here we know that parabola is passing through three points (0,0), (11,3) and (16,0) and we also know…

Q: 6. Center at (2,-3), one corner of auxiliary rectangle at (-1,-5), conjugate axis is horizontal

A: Given: Center: (2, -3) One corner of auxiliary rectangle at (-1, -5), conjugate axis is horizontal.…

Q: Find the equation of the plane con taining the points Р(4, -1, 3) Q(1, -2, -1) and R(1, 0, 8)

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Q: The plane that passes through the point (5,2,2) and is perpendicular to both x-5z=-24x-5z=-24 and…

A: The direction ratio of the normal vector to the plane x-5z=-24 or x+0y-5z=-24 is (1,0,-5) The…

Q: The equation of a circle with center (2,8) and radius 10 is O (2- 2)+ (y- 8)' = 10 O (2 + 2) + (y-8)…

A: Equation of a circle with centre (a,b) and radius r is given by (x-a)2+(y-b)2 = r2 here a = 2 b = 8…

Q: In the xy-plane, line k intersects the y-axis at the point (0, –6) and passes through the point (2,…

A: Given:- In the xy-plane, line k intersects the y-axis at the point (0, -6) and passes through the…

Q: . Find an equation of a plane passing through the point (3, 4. 0) and containing the line of…

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Q: Find an equation for the set of all points (r, y, z) equidistant from point 10.) (1,0, 2) and the…

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Q: Write equations for the circles with radius 5 containing the points (-1, -4) and (4, 1). How many…

A: Given: The circles with a radius(r) is 5 containing the points (-1,-4) and (4,1) Then we have to…

Q: quadrilateral

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Q: Find the parametric and symmetric equations for a line that passed through the points (2,0,8) and…

A: Representing the points as the points vectors we get,  2,0,8 and -2,6,4 The direction numbers are…

Q: The coordinates of the point in the first quadrant where the line with equation y = 1.5z + 4…

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Q: Find an equation of a line containing the point (1, 7, -3) and parallel to the yz- plane.

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Q: Equation of the circle with center (-4, 9) and radius 8 is

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Q: Calculate the distance between the points K=(-9,7) and M=(-4, 2) in the coordinate plane. Give an…

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Q: The drone starts at point (0, 0), the landing pad is at point (11, 3) and the parabolic path must…

A: Given

Q: Find an equation of the plane that passes through the point (18, -16, 9) and contains the line given…

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Q: Charlie and Alexandra are running around a circular track with radius 60 meters. Charlie started at…

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Q: Find the distance between the point (1,3,-1) and the plane 3x - 4y + 5z = 6. (Enter an exact answer…

A: Given point 1,3,-1 and the plane 3x-4y+5z=6

Q: A radio signal can transmit messages up to a distance of 5 km. If the radio signal's origin is…

A: Given that radio signal can transmit messages up to a distance of 5 km origin = (-2, 7)

Q: Through the point (2, -4, 0) and parallel to each of the planes 2x + y -z = 0 and x+ 5y + 3z = 0.

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

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Q: A circle in the xy-plane has a diameter with endpoints (-1, 3) and (7,3). If the point (0,b) lies on…

A: Topic = circle