Transform the general form x^2+y^2 +2x -6y -15 =0 of a circle into standard form. * (x+1)^2+(y-3)^2=25 O (x+2)^2+(y-3)^2=9 (x+3)^2+(y+3)^2=25 O (x+1)^2+(y+7)^2=9

Q: Find the coordinates of the vertex of the parabola y = x^2 - 4x + 1 using derivatives O (2, -3) O…

A: To find the vertex of the parabola by using derivatives

Q: Finally, determine a. The parabola passes through the point (0, 5). Substitute the values of x and y…

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Q: Find the vertex of the parabola Y= 6X^2.+24X + 18 O (6, 2) O (2, 6) O (2,-6) O (2, 6)

A: We have to find

Q: Consider the hyperbola 85.3166x² – 4y² = 1365.07. -

A: We have to find the foci of the given hyperbola.

Q: Identify the graph of the nondegenerate conic sections: 4x2 - 25y2 - 24x + 250y - 489 = 0.

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Q: 6 Write the equation in general conic form of the circle with center (2, 3) and r = 7 x 2 + y 2 -…

A: To write the equation of circle with the given center and radius.

Q: There is a parabola which has a minimum where the two lines 3x+6y-1=0 and 2x+ y-2=0 intersect. The…

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Q: 15. x2 - 8x + 2y + 10 = 0

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Q: A parabola of y=x^2 has been regraphed and now sits with each side plotted at (-3,5) and (3,5) and…

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Q: 7. Determine all values of a that will cause the parabola y=ax² +10x+1 to cross the x-axis at two…

A: 7) y=ax2+10x+1 ...................eq (1) For parabola to cross the x- axis put y=0 0=ax2+10x+1…

Q: Show that the equation 7x^2 + 48xy -7y^2 + 20x -110y -50 = 0 is a hyperbola using the matrix method…

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Q: transform into standard form of hyperbola x^2-y^2+6x-4y-4=0

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Q: Write an orthogonal change of coordinates converting the equation of the conic 3x2+3y +3z+2ry+2rz…

A: Given equation , 3x² + 3y² + 3z² + 2xy + 2xz+2yz = 1

Q: 3. Where do the asymptotes intersect for the hyperbola y = ( 2x +3 ) / ( 8x +5 ) O ( 3/8 , 2/5 ) O…

A: Given : Hyperbola y =2x + 38x + 5   To find the asymptotes.

Q: 2- Write the equation of hyperbola that pass through point (12, 9) and have F1 (0, 0) and F2 (0, 4)V

A: Consider the given information. y−k2a2−x−h2b2=1 Since we have the given foci at F1(0,0) and F2(0,4).…

Q: 12. 9x²-16y -90x+64y+17 = 0 | 2. 250-

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Q: Write the general conic form equation for a circle with center (3, -1) and radius of 5. x 2 - 6x +…

A: We can find the general form of conic form equation as below.

Q: 18. Identify the surface that corresponds to the equation 100y^2 - 25x^2- 4z^2 = 1. show solution

A: It represents hyperboloid.

Q: 12. Use vertex form to write the equation of the parabola. y= 3(x+2)° +2 y= 3(x- 2)° +2 y= 3(x- 2)°…

A: best and easiest way is one by one checking if the given option satisfy the given points (-2, 2) and…

Q: Any point on the parabola can be labeled (x, y), as shown. 4 3 2 (*, y) ¢ -6 -5 -4 -3 2 - 1 2 3 4 5…

A: According to figure equation of parabola in standered form X2=4bYnew equation of…

Q: 7. Find the centroid of a triangle whose vertices are (2, 3), (-4, 6) and (2, -6). В. (0, -1) A. (0,…

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Q: 8. Write the parabola y- 6y + 16x + 25 = 0 in standard form.

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Q: What is the equation of a parabola that intersects the x-axis at points (-1, 0) and (3, 0)?   A. y…

A: Given that: A parabola intersects x-axis at (-1, 0) and (3, 0)

Q: Determine the hyperbolic form of L-

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Q: Identify the x-intercept(s) of this parabola. 10 8- 6- 4- -6 -2 2. 6 -4 O (3. 0)

A: x-intercept is the point where the graph crosses the x-axis.

Q: Differentiate. Show all work. a. у y%3D3@-2x Зе

A: Since you have asked multiple questions in a single request, we would be answering only the first…

Q: 17. Explain why it is not possible for a line in three-space to be represented by a scalar equation…

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Q: The point (1,2) lies on the parabola: y 3x2 -2x+2 %3D

A: Thanks for the question :)And your upvote will be really appreciable ;) False statement (1,2) does…

Q: 5. What is the standard for equation of a parabola with its vertex at (0,0) and a directrix of x-3?…

A: Given: A parabola has vertex 0, 0 and directrix x=3      ……1   To find: Equation of parabola

Q: A rectangle has its two lower corners on the xx-axis and its two upper corners on the parabola…

A: Topic:- application of derivatives

Q: How to convert 3y^2-x^2-9=0 into standard form? I know it is a hyperbola.

A: Answer and explanation is given below..

Q: Identify the graph of non-degenerate conic whose equation is: x2-8x-12y=44

A: Explained below

Q: Find the equation of a parabola that has a vertex of (-2, -1) and contains the point (0, 3).…

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Q: 4. (5) Find the equation of the plane passing through the points. Simplify the equan (2,0,1),…

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Q: Suppose that the only barrio is located at the center of a circular field. If a researcher needs to…

A: (a) We know that distance between two points O (x1 , y1)   and   A(x2, y2) is given by formula,…

Q: Show that the line b2xx1 - a2yy1 - a2b2 = 0 is tangent to the hyperbola b2x2 - a2y2 - a2b2 = 0 at…

A: Find dy/dx.Then find dy/dx at the point (x1,y1) by plugging x=x1 and y=y1

Q: 4x^2 - 3y^2 + 12z^2 + 12 = 0

A:

Q: Identify the graph of the nondegenerate conic sections: 9x2 + 25y2 - 54x + 50y - 119 = 0.

A: First we need to identify that the equation represents which conic section:   We have:…

Q: 2. A parabola with axis parallel to the x-axis and passing through (5,4), (11, –2) and (21, –4)

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: I noticed that depending on the values for A and C,assuming that they are not both zero, the graph…

A: Depending on the values for A and C, assuming that they are not both zero, the graph of Ax2 + Cy2 +…

Q: The parabola y + 2y + 8x –7=0 has vertex at O (-1, –1) o (-1,1) о (1,-1) о (1,1)

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Q: Identify and sketch manually the graph of the quadric surface 25x² -25y² -9z²-150x + 200 = 0.

A: Solution :-

Q: Identify and sketch the graph of the quadratic surface 4x2-y2-z=1

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Q: 2- Write the equation of hyperbola that pass through point (12, 9) and have F, (0, 0) and F2 (0, 4).

A: Since, the foci of the given hyperbola are F′(0,0​) and F(0,4​) which lie on the X-axis and…

Q: I graphed 2x2 - 3y2 + 6y + 4 = 0 by using the procedure for writing the equation of a rotated conic…

A: The given equation is  2x2 - 3y2 + 6y + 4 = 0 . Note that there is no xy terms in the above…

Q: Identify the center of the conic section whose equation is 4x 2 - 25y 2 - 8x - 100y - 196 = 0. (-1,…

A: We can identify the center as below.

Q: Match the parabola to an equation in standard form. 2+ -4 -2 4 6. Ta-1) -4- (x-1)2 = 4(y+1) (x+1)2 =…

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Q: Sketch the hyperbola. (x – 9)2 - (y – 3)² . 16 4 y y 15 15 1아 10 15 -10 -5 5. 10 15 15 -10 -5 10 15…

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Q: The parabola x² - 2x + 2y + 7 = 0, has a vertex at (1,3). O(-1,3). O (-1,-3). O (1,-3).

A: Suppose the equation of a parabola is of the form  y=ax2+bx+c where a, b and c are constants. The…

Q: The equation of a surface, with respect to an orthonormal coordinate system for three-dimensional…

A: Every surface equation with respect to an orthonormal coordinate system is written in a matrix form…