4. Endpoints of its conjugate axis at (0,-3) and (0,3) and one focus at (5,0)

Q: Find a parametric equation of the line passing through the point (3,-1,-3) and perpendicular to the…

A:

Q: 3Q: If z₁ = 1.5 cisand z₂ = 4 cis(-7) find and express it in the rectangular form.

A:

Q: Find parametric and symmetric equations for the line satisfying the given conditions. Through the…

A:

Q: What is the image of the point (4, 5) after a rotation of 90° counterclockwise about the origin?

A: Given data: The given coordinate of x is x=4. The given coordinate of y is y=5. The given angle in…

Q: Identify the conic withthe given equqtion and give its equation in the standard form.2xy+2√2x-1=0

A: Given  the equation of the curve  2xy+22x-1=0 we need to find the conic and its equation in the…

Q: Find a parametric representation of a straight line through (1,1,1) and (4,0,2), and sketch it.

A:

Q: find parametric and symmetric equations for the line through (1,-1,2) and parallel to the line…

A: From the line x+2=y-1=z  we get the direction ratio=(1,1,1)The direction ratio of the parallel line…

Q: What is the image of the point (-2, 4) after a rotation of 270 counterclockwise about the origin?

A:

Q: A flashlight is shaped like a paraboloid and the light source is placed at the focus so that the…

A: Given the flashlight is shaped like a paraboloid and the light source is placed at the focus so that…

Q: 33. Find parametric equations for the path of a particle that moves along the circle x² + (y – 1)² =…

A: from the equation of a circle given to us, we have the radius r = 2 as the general form of the…

Q: What kind of conic section is given by the quadratic form ? -11x,2 + 84x,x2 + 24x,2 = 156 Transform…

A: Given Quadratic Equation is, -11x12+84x1x2+24x22=156 Matrix Representation form is, A=-11424224 Find…

Q: Consider the point at (2,4). Suppose you rotated the point 30 degrees counterclockwise about the…

A:

Q: Find the slope of the line tangent to the conic section 25 (x+3), (y+2)² = 1 at (3,8). 36

A: We find the slope of tangent to the given conic with the help of calculus .

Q: Identify the type of conic from the discriminant.Xy-2 = 0 , =45

A:

Q: 5. Find the exact value of distance from the point (1, -3, -1) to the plane 2x-y+3z = -5

A:

Q: 33. Find the directrix. (y- 9)2 - 8 O y = -9 O y = -7 O x = -7 | x = -9

A:

Q: By differentiating implicitly, find the slope of the hyperboloid x² + y? - z2 = 1 in the x-direction…

A:

Q: 12) The distance from the point S(-10, –4, –6) to the plane -9x + 2y + 6z = 4

A:

Q: 2. x = --(y+ 4)² + 5 y Vertex: Opens: Focus: Directrix:

A:

Q: find the equation of the tangent line through the point (2,-2) to the hyperbola x2-y2=16.

A:

Q: 2. Find an equation of the sphere that passes through the point (2, 3, –1) and has center (-3, –1, –…

A:

Q: 7. Find the distance between the point (- 3, 2, 1) and the plane with equation x - 2y + 3z = 5

A:

Q: y -6- 4- 3- 2- 1- -3 2 -1 0 12 3 4 5 6 -1- -2- R -3- your work on question 10, classify this…

A:

Q: the sum of the distances from (x,y) to (-1,0) and from (x,y) to (1,0) is 4. show x and y is related…

A: Distance from (x,y) to (-1,0) is:  Distance from (x,y) to (1,0) is:

Q: 5. Find parametric equations for the line through the points (1, 3, 0) and (2, 4, 4).

A: 5. Given that, the points are 1,3,0 and 2,4,4. Note that, the symmetric equation of the a straight…

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: Find an equation for the set of all points equidistant from the point (0, 0, 2) and the xy-plane.

A: Let any such point is given by (x,y,z)(x,y,z) is z units away from the xy plane.

Q: 2: (a) Find parametric equations for the line through the point (-6, 1,2) and the point of…

A:

Q: Determine the length of the latus rectum of the following conic section: 16z + 9y? - 64.x- 54y+1 0 O…

A: 16x2+9y2-64x-54y+1=016x2-64x+9y2-54y=-116(x2-4x)+9(y2-6y)=-116(x2-4x+4)+9(y2-6y+9)=-1+64+8116(x-2)2+…

Q: What kind of conic section (or pair of straight lines) is given by the quadratic form Q(x1, x2) = x…

A:

Q: Show that the “conic section” with equation x2 − 4x + y2 + 5 = 0has no points.

A: Equations for conic sections are obtained as the locus of points following one or a set of…

Q: 9/5 Directrix x + 2, center at (2, -6) and one of vertices at (2, -4). 5 %3D

A:

Q: Use a translation of axes to put the conic in standard position. Identify the graph, give its…

A: First, we write x and y terms together, so it becomes, x2 - 4x + y2 - 4y = -4 By using completing…

Q: 2. x = --(y+2)² + 7 Vertex: Opens: Focus: Directrix:

A: Given,  x = -14y+22+7   We have to find vertex, opens, focus and directrix. and graph the function.…

Q: 3. Through the point (4, -5, 20) and perpendicular to the plane x + 3y – 6z - 8 = 0.

A:

Q: 4 - Find an equation of the Planc perpendicular to each of the planes X-y +2=0 and 2x ty - 4z -5 =0…

A: A detailed solution is given below

Q: 1. Which Is the corresponding equation of a hyperbola with co-vertices at (0, -6) and (0, 6) and a…

A: Given, The co-vertices of the hyperbola are 0, -6 and 0, 6  and transverse axis is 20 units long.…

Q: Find the slope of the line tangent to the conic section 25 (х-2)2 (y-6)2 = 1 at (2,10). 16

A:

Q: (x + 3)² 64 - - (y – 5)² = 1 - Distance from the center to each focus is:

A:

Q: Find 3 non-collinear points in the plane ax+by+cz+d=0. (Hint: Set two variables to zero for each…

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

Q: Find parametric equations and a parameter interval for the motion of a particle that moves along the…

A:

Q: Which of the following is the equation with center (-9, 8) Major axis = 10? %3D 20 and minor axis…

A: To find the equation of the vertical ellipse with center (-9,8) . Major axis = 20 and minor axis =…

Q: find parametric equations for the given curve. Line through (3, 1) and (−5, 4)

A:

Q: Find the equation of the plane containing the x-axis and passing through the point (4,3,1/5)

A:

Q: 12. Find the distance between the point (3,-2,7) and the plane 4x – 6 y + z = 5.

A: The equation of plane is 4x-6y+z=5 and the given point is 3,-2,7. The distance between the point and…

Q: 3. Find equations of both the tangent lines to the ellipse x²+4y?=36 that pass through the point…

A:

Q: 3. Find the parametric equation of the line passing through the point (-1,0,3) and in the direction…

A:

Q: Parametrize the line segment joining the points P(-3, 2, -3) and Q(1, -1, 4)

A: we have to parametrize the line segment joining the points P(-3,2,-3) and Q(1,-1,4)   as we know…

Q: 5. Find the distance from the point (4, -3, 6) to the plane *-2y+z=1

A: