Find the radius and center of the sphere. [Hint: Complete the square in each variable.] x? + y? +z? - 4x– 4y + 6z = - 1

Q: 8 m A. 55 m² B. 110 m² D. 44 m² Translate the equation below into standard form using completing the…

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Q: 1. Put the following equations in standard form and find the center point and the radius: a) x-2x+y…

A: Given that

Q: Find the endpoints points of the lactus rectum for (y-3)^2=8(x+1)

A: Given problem:- Find the endpoints points of the lactus rectum for (y-3)2 =8(x+1)

Q: Find the radius and center of each sphere. [Hint: Complete the square in each variable.] x2 + y2 +…

A: The general equation of the sphere is given as x-x02+y-y02+z-z02=r2. Here, the center of the sphere…

Q: Q3: a\ A triangle whose vertices are A = (-1,0), B = (2, 1), and C = (1, -2), find:

A: Solution

Q: Find the area of the triangle which the line 2x – 3y + 6 = 0 forms with the coordinates axes. a.3…

A: First we find out x intercept and y intercept of given line and solve it.

Q: ²+y? + - 2x – 4y + 8z + 17

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Q: y A A -4 -2 4 В 6 x -2 C 42. Show that the triangle with vertices A(6, -7), B(11, -3), and C(2, -2)…

A: Given vertices of △ABC: A=6, -7B=11, -3C=2, -2

Q: Find the Center and radius of the Cirele x?+y²+4X-6y -320

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Q: • Which of the following equations has a graph of a sphere? a. x2 + y? + 2² +x + y+ z + 3 = 0 b. x?…

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Q: The distance, d, between the points (X1, y1) and (x2, y2) in the rectangular coordinate system is d…

A: To find: The distance, d, between the two points (x1, y1) and (x2, y2) in the rectangular cordinate…

Q: 11 What are the coordinates of the center and the length of the radius of the circle represented by…

A: Given that a equation circle and we find coordinate of circle center and radius. We know that the…

Q: How far is the center of the circle x2 + y2 – 8x + 1 = 0 from the x-axis? a. 2      b.  0…

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Q: Complete the square to write the following equation as standard equation of a sphere and find center…

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Q: Three of the coordinates of a square ABCD are A(3,2) C(1,-2) and D(0,1). What is the y-coordinate of…

A: That's easy. Have a good day!!!

Q: Find the center and the radius of the sphere. x2 +y? +z? +5x + 6z = 0

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Q: Show that the given equation represents a sphere and find its center and radius x² + y2 + z? + ax +…

A: The given equation is x2+y2+z2+ax+by+cz+d=0. The general equation of a sphere with center h,k,n and…

Q: Which of the following point is the closest point on the sphere a? + y? +2? = 4 from the point…

A: In this question we have to find the point that is closest point on the sphere.

Q: Find the center and the radius of the sphe- x2 +y? +z? + 6x – 4z = 0

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Q: Write an equation of a circle whose center is (0,0) and radius is 5 O 2² + y? 25 O (z) + (y – V5)? =…

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Q: Imu the cördihates of the center and the radius of the circle. 8. x + 10x + y² + 4y + 24 = 0 9. x -…

A: Compare with standard form of circle

Q: Find the radius and center of each sphere. [Hint: Complete the square in each variable.] x2 + y2 +…

A: Find the radius and center of each sphere. [Hint: Complete the square in each variable.] x2 + y2 +…

Q: Complete the square to write the following equation in the standard form for a sphere. x²+y²…

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Q: 3 Which equation is for the hyperbola? O x = a (y – k)² + h (z-h)² (y-k)? = 1 O (z – h)° + (y – k)°…

A: LET'S FIND HYPERBOLA EQUATION,   ANSWER :-  OPTION B IS RIGHT   OPTION A IS PARABOLA. OPTION C IS…

Q: Find the equation of the parabola y = ax? + bx + c passing through the points (0, 6), (- 2, 2), and…

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Q: Complete the square to find the center and radius: x^2+y^^2+8x+8y=0

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Q: The quadrilateral below is a trapezoid Find GH. 19 B G H. 9x- 3 5x + 1 E GH = %3D

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Q: Find the point on the sphere x? + y² + z² = 3 farthest from the point (-6, 6, –6). Farthest point is

A: Given equation of the sphere, Given point is (-6, 6, -6). Distance of the point (-6, 6, -6) from…

Q: 8: Which one of the following conics is a parabola? 22 + y + 5 = 4æ B 222 + y? = 4x +4 4r – 9y? +…

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Q: Determine the value of x and y in the isosceles trapezoid. x + 2 Зу 8 5y - 2 3x + 4

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Q: Identify the center and radius of the circle. x2 + y? – 4x + 10y – 7 = 0 %3D

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Q: 9. The equation of the hyperbola is of the form (x – h)? (y - k)² (a) a? (y – k)? (x - h)² (b) a? (x…

A: Answer: (a) (a)(x-h)2a2-(y-k)2b2=1(b)(y-k)2a2-(x-h)2b2=1

Q: The three-dimensional quadric figure below is described by: x² + 2y? + 2z – 5 = 0

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Q: CLO 4 If the plane x+y+z-6%3D0 cuts the x-axis, y-axis, and z-axis at A, B, and C respectively. Find…

A: first we will find the coordinates of the points A B and C then find the length of the sides (AB,…

Q: Find the point on the sphere x2+y2+z?=7056 that is farthest from the point (5,-15,-2)

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Q: 5. The equation x² + y? + 2 y +z2 - 2 z = 0 is a sphere. Determine its center and radius.

A: Follow next step

Q: III. Transform the equation of the parabola to the standard vertex for: completing the square. 16.…

A: Since we are given with multiple number of question and our guideline is solve first question only…

Q: Find the standard form for the equation of a circle (2 – h)² + (y – k)² = r? with a diameter that…

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Q: Which of the following point is the farthest point on the sphere a? + y² + z? = 4 from the point…

A: The equation of sphere is given as, From the equation it is clear that the sphere has its center at…

Q: (c) 6.x-40y dA, Dis the triangle with vertices (0,3), (1.1), and (5.3)

A: The vertices of the given triangle are (0, 3), (1, 1)1 and (5, 3).  Let us take consider the three…

Q: z-3V AVWX is a right triangle with altitude WU. What is XV? W 5 8 10 1/2

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Q: where C is the square with corners ±(1±i) [0). [0).

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Q: Y 2- Given ABCD is a, isosceles trapezoid, Find the coordinates of point C. В (а,b) C(..) A(0,0) D…

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Q: Find the point on the ellipse x? + 4y? + 2xy = 12 with the greatest x-coordinate. (Use decimal…

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Q: On the lacrosse field, the circular region around the net, called the crease, is an area that only…

A: Concept : equation of circle with center xo,yo and radius r is (x-xo)2+(y-yo)2 =r2 the crease can be…

Q: The distance, d, between the points (x1, y1) and (x2, y2) in the rectangular coordinate system is d…

A: Two points are given as, x1,y1  and  x2,y2 .   Now Using the section formula to obtain the distance…

Q: find the ends of the latus rectum, axis of symmetry of x2+20y=0

A: Given  x2+20y=0 Find the ends of lactus rectum and axis of symmetry.

Q: How long is the latus rectum of the parabola y? + 3x – 12 = 0? O 12 O 6 4 O 3

A: The given parabola is: y2+3x-12=0

Q: Match the quadric surfaces to its graph. A. y? + 22 = 4 + 4x? C. 9x? + 4y? = 36 + 36z2 B. 4x2 + y? +…

A: This is a problem related to the curve plotting in the 3 dimensions. Based on the available concepts…

Q: A circle has the equation (z+1) + (y - 3)? = 16. What are the coordinates of its center and the…

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