7:+1 The singular point/s of f(=)= in the region ellipse =-3:-4 x² + 4y2 = 4 is/are A) -1 B) 4 C) 4 & – 1 D) 2

Q: 20. Find the foci of the ellipse with the following equation: 169 + = 1 25 O F(-5, 0), F2(5, 0) O…

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Q: The plane x + y + 2z = 2 intersects the paraboloid z = x² + y² in an ellipse. Use Lagrange…

A: Note that here we have to extremize x2+y2+z2 , whch is eqivalently ,to extrimize x2+y2+z2.

Q: Determine the point on the plane 2x + 3y − 4z = 0 that is closest to the point P(1, 1, 1)

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Q: (a) Find the center and radius of the sphere defined by x² + y² +2²-8x + 2y + 8 = 0. (b) Find the…

A: A sphere is object that is 3-D analogue to a 2-D circle. If its center at the point (a, b, c) and…

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: Derive the equation of the parabola with a focus at (2, 4) and a directrix of y = 8. 1 O f(x) -(x –…

A: Given query is to find the equation of parabola.

Q: What is the center of the sphere given by the equation x² − 6x + y² – 2y + z² + 8z + 17 = 0? -…

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Q: Find an equation for the sphere with center at (-7,8,0) and radius = 9 O x2 + y? O x2 + y2 + z- -…

A: We have to find

Q: 5. Sketch the parabolas showing the intercept and the maximum/minimum points. a) y = 2x – 4x +7 b)…

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Q: Find the area of each circle, given the radius r or the diameter d. Leave your answer in tems of t.

A: See the detailed solution below.

Q: Q4) Find the intersection of the line x = and the sphere x? + (y – 3)² + (z – 2)² = 4. A) (1,1,0) B)…

A: 1. In analytic geometry, a line and a sphere can intersect in three ways: No intersection at all…

Q: 13) Find the equation in slope-intercept form that is tangent to (x- 1)² + (y + 2)² = 25 and passes…

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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: P(x, y) is any point on the ellipse 16x\power{2} + 25y\power{2} = 400 and F\index{1}=(3,0),…

A: We have 16x2 + 25y2=400         or      x225+  y216=1        or       a2=25 and  b2=16

Q: formed by points of intersection of ellipse (B) Area of quadrilateral 2 2 x² + y² - xy + x - 4y - 12…

A: Given,  x2+y2-xy+x-4y-12=0 We have to find the area of quadrilateral formed by points of…

Q: Give equations for two distinct planes whose trace in the xy-plane hasequation 4x + 3y = 8.

A: Given information: The xy-plane has equation 4x + 3y = 8. Calculation: The equation of the plane is…

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: v = (2x² – y² +4)i+(5y+3x – 6)j . Consider two closed paths starting (and ending) at a dock located…

A: Let A=(-1,0), B=(2,0), C=(0,2). Now,∫path 1v.dr =∫path 12x2-y2+4dx+5y+3x-6dy…

Q: If ƒ (§) = $c 4z²+z+5 dz, where C is the ellipse 12+ 2 = 1 z- 4 9 Find ƒ(i),ƒ(i),ƒ'(−1) and ƒ"(−1)

A: Step 1: Given function is:                                                   f(ξ)=∮C​z−ξ4z2+z+5​dz…

Q: All the chords of the hyperbola 3x² – y² – 2x + subtending a right angle at the origin, pass thr…

A: Introduction: A rectangular hyperbola can be defined in a number of different ways. We can use any…