Given the equation of all points equidistant from a center, what is the center point? (x – 3)² + (y – 5)² = 12

Q: For Exercise, find an equation of the form  y = ax2 + bx + c that defines the parabola through the…

A: Consider the given equation of parabola:

Q: Find the standard equation of all circles having center at a focus of 52 7(x+2)? (y-3)2 = 1 39 and…

A: Let's find.

Q: Determine the equation of the directrix of the curve 3x=2y2-4y+7 a. x=30/20 b. x=30/24…

A: Solution: The given equation is 3x=2y2-4y+7

Q: 5. Find the equation for the sphere whose center is at (-1, 1/12-13) and radius is

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Q: Find the maximum and minimum values of the function f(, y) = xy on the ellipse given y? by the…

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Q: Given a focus of (2, 4) and a directrix of y= -2, find the equation for the parabola. (2-

A: Given:    focus (2 , 4)    directrix y = -2

Q: Find an equation of the line containing the centers of thetwo circles x2 + y2 - 4x + 6y + 4 = 0 and…

A: The given circle equations are x2+y2-4x+6y+4=0    and   x2+y2+6x+4y+9=0. Compare the above circle…

Q: In the equation 3x2 + 4y2 -18x + 8y +19 = 0, find the center and foci, plot the ends of the axes and…

A: 3x2+4y2-18x+8y+19=0 On simplification, we get…

Q: Find the value of Y for the hyperbola defined by the equation y² – x² = 7 at the point (3, 4). dx2

A: The equation is y2-x2=7. First find the value of dydx as follows.…

Q: 6. What is the equation for the slope of the ellipse+= 1 at (x₁, yi)? A. B. C. D. E. y' = y' = b²y₁…

A: We have to find the equation of the slope of ellipse at the point (x1,y1).

Q: Which of the following is a point of intersection of a circle and an ellipse with the respective…

A: Question is solved.

Q: The parabola y=x^2+13 has it's focus at the point (b,c) where  b= c=

A: The given equation of the parabola is, y = x2+13. Also the parabola has its focus at (b, c).Consider…

Q: Find the equations of the osculating circles of the ellipse 25x2 + 4y? = 100 at the points (2,0) a.…

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Q: The figure shows a lamp located three units to the right ofthe y-axis and a shadow created by the…

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Q: Which of the following correctly depicts the sphere given by the equation: x2 + (y - 2)2 + (z - 2)2…

A: Given: x2 + (y - 2)2 + (z - 2)2 = 4

Q: What is the equation of the line tangent to the hyperbola = 1 at the point (V2a, b)? y = -a+b 26 V26…

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Q: In a simple video game, a rocket travels in an elliptical orbit whose path is described by the…

A: Given, Equation of the ellipse 4x2 + 25y2 = 100 Now, rocket is travelling to the tangent to its path…

Q: 1. A circle has this equation. x² + y² + 4x – 10y = 7 What are the center and radius of the circle?…

A: To find the radius and center of the following circle  x2 + y2 + 4x - 10y = 7

Q: c) Find the center and radius of the sphere whose equation is x² + y² + z² + 10x + 4y + 2z – 19 = 0

A:

Q: State whether the given equation defines an elliptic paraboloid, a hyperbolic paraboloid, or an…

A: 3x2-7y2=z On simplification, we get ⇒z=x213-y217⇒z=x2132-y2172⇒z=x132-y172

Q: Q1. Find the equation of sphere whose center is at (4,-1, 7) and radius is 5.

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Q: F. dr, where C is the ellipse (x + 3)² + 5(y – 2)² = 16 and F(r, y, z) = x²i +y²j+ z²k.

A: The vector field is Fx, y, z=x2i+y2j+z2k. The curve C is x+32+5y-22=16. Obtain the parametric…

Q: Find an equation of the parabola that satisfies the given conditions.Focus F(2, 0), directrix x = -2

A: If the coordiantes of the focus h+p,k and directrix x=h-p Then, equation of parabola y-k2=4px-h We…

Q: A parabola has an equation of y² = 4x. Find the nearest distance from the point (-3, 6) to the %3D…

A:

Q: Given the general form of a parabola x2+8x-12y+11=0, what is the equation of the directrix? y=_____.…

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Q: Find the center (h, k) and radius r of the circle with the given equation. 4x2 +4y2 - 12x + 16y - 5…

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Q: Find an equation of the line containing the centers of the two circles x2 + y2 + 2x + 2y + 1 = 0 and…

A: Given,

Q: Find the equations of the osculating circles of the parabola y = 3(x – 2)2 at the points (2,0)

A:

Q: 1. For the parabola equation: (y-2) = -3(x+4)^2 + 7, in which direction does the parabola open? *

A: We have to find the direction in which the given parabola opens.

Q: For Exercise, an equation of a hyperbola is given. Determine whether the transverse axis is…

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Q: Find the coordinates of the four points at which the hyperboloid of one sheet given by x2 y? + 16 z?…

A: This question is related to 3D coordinate geometry, We will solve it using given information.

Q: 2. Write the general equation of the parabola with directrix at x FG,-1), and v (. -1). 2

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Q: Find equations of both the tangent lines to the ellipse  x2 + 7y2 = 63  that pass through the point…

A: consider (x0 ,y0) be an any point on ellipse

Q: Find the following points of intersection. The point(s) of intersection of the parabola y = x2 + 2…

A: Given equation of parabola is y=x2+2 and equation of line is y=x+4. We have to find point of…

Q: find a cartesian equation for the curve r2cos(2θ)=1

A: r2cos2θ=1

Q: (3) Find the coordinates of the points of intersection of the parabola y = x2 - ax and the line y =…

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Q: ^2+84x-24y

A: Given Ellipse: 21x2-4y2+84x-24y=36This equation can be re-written as-21(x2+4x)-4(y2+6y)=36 To find…

Q: x ds, where C is the portion of the parabola from (0,0) to (1, 1), followed by the line segment from…

A:

Q: Given a focus of (4,5) and a directrix of y=-3, fınd the equation of the parabola. y = (x –

A: We need to find equation of parabola.

Q: What is the second coordinate of the center of the sphere of the equation below?…

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Q: Find the equation of Parabola and Graph with the following information: Center at (0, 0) Vertices…

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Q: Find an equation of the paranola in standard form: with the vertex at V (2,-4) and directrix y= -5

A: Find an equation of the parabola in standard form: with the vertex at V (2,-4) and directrix y= -5

Q: By differentiating implicitly, find the slope of the hyperboloid 22 + y? – 22 = 1 in the x-direction…

A: We have to find slope of the hyperboloid x2+y2-z2=1 in the x-direction at the points (a) 1,2,2 (b)…

Q: A hyperbola has an equation of 2x² – 5y² = 10. If the equation of the hyperbola is equal to x – 5y =…

A: The given equation of the hyperbola is: 2x2-5y2=10 Differentiating both sides of the equation with…

Q: c) Find the center and radius of the sphere whose equation is x² + y? + z? + 10x + 4y + 2z - 19 = 0

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Q: Find the equation of the parabola y = ax^2 + bx +c that passes through the points (-1,-4) (1,4), and…

A: topic  -  parabola

Q: Given the equation, (x-h+v-k)² =r?,what are the coordanates of the center? The coordinates of the…

A: Answer and explanation is given below....

Q: The signal received by a parabolic antenna is concentrated in its receiver, which is placed,…

A: For the Paraboloid,z-axis is it's Principal Axis,Also, it is symmetric with the lines x = 0 (yz…

Q: The equation of the hyperbola whose foci are (-2,0) and (2,0) and length of transverse axis is 2 is…

A:

Q: find a cartesian equation for the curve r=3cos(θ)

A: Cartesian equation for the curve is r=3 cos(θ)   Now x=r cos(θ)  …….. equation(1) cosθ=xrr=3xcosθ…