The standard equation of the sphere that has center (1,-2,1) and passing through the origin, is given by Px+1)²+(y-2)²+ (z – 1)² =6 Ox +1)2+(y-2)²+ (z – 1)² = 36 O (x-1)2 +(y+2)² + (z–1)² =6 (x-1)? +(y+2)² + (z+1)? = /6

Q: (x − 6)²(y+3)² + 36 25 = 1

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: a) y = (x - 4)² b) у 3 (х — 2)2 -4 c) y = (x + 3)² – 2

A: (a) In the given equation y=(x-4)2, At x=0 and x=8, y=16 At y=0, x=4. Thus, the x-intercept of the…

Q: What specific (include direction/opening and vertex/center) conic section is 4x + y + 72x + 14y +…

A: topic- algebra

Q: Find the equation of the sphere with center c= (0, -1, 2) and radius r= 5. O x2 + y + 1)2 + (z + 2)2…

A: Biref answer is given below.

Q: Find the equation of the hyperbola with vertices (- 3, 2), (5,2) and foci (- 4,2), (6,2) O (x- 2)2…

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Q: Arrange the parabolas represented by the equations according to the positions of their foci on the…

A: The standard form of a parabola is  (x – h)2 = a(y – k) where (h, k) is the vertex.

Q: 12) (x − 8)²(y+7)² - + 100 25 (x + 2)²_ (y − 1)² 4 64 YG X 14) = 1 G = 1

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Q: Find the center of the ellipse 16x² +9y² - 64x - 54y + 1 = 0 (a)_(-2, 3) (b) (-2, -3) (c)_(2, -3)…

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Q: What are the foci of the ellipse given by (z-3)2 (y-1)2 - = 1? 25 O (-4, 1) and (4, 1) O (3, 5) and…

A: Topic : foci of an ellipse

Q: 2) The diameter of a sphere has endpoints given by points P = equation of the sphere in standard…

A: The diameter of a sphere has endpoints given by points The Equation of sphere whose center and…

Q: A laser pointer is situated at the point (3, 1, 4) and is pointing a linear beam in the direction…

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