1. Find the isogonal trajectories intersecting at an angle 45° to the family of the hyperbolas x2 - y2 = c x + 3xy - y =c x2 + 2xy - y? = C 2х + ху - у %3 с y + x = c 2. Find the orthogonal trajectories of the family of parabolas y2=4ax. 2x2+y? = c 2y2+x? = c x2-2y? = 2x2-y? = c

Q: Find the parabola of the form y=ax^2+b which best fits the points (1,0), (4,4), (6,8) by minimizing…

A:

Q: y2 = 20x О А. (5,0), х - -5, у-аxis В. (5,5), х%3D5, х-аxis С. (5,0), х%3D — 5, х-аxis D. (0,5), y…

A: Given query is to find the the focus , directrix and symmetry for the parabola.

Q: Consider the equation z = x² + y. (a) Describe the traces of the equation parallel to the xz-plane,…

A:

Q: 5) Find the unique quadratic curve (i.e. parabola) which passes through the following three points:…

A: We have to find the unique quadratic curve which passes through the following points:…

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: 3. Find the vertex for the parabola 4x + 2y² + 8 = 0. (a) (0, -2) (b) (-2,0) (c) (2, 2) (d) (-2,1)

A: The equation of the parabola is  4x+2y2+8=0

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: 13. Which of the following is the equation of the graph shown? 2 Parabola Oy = - 3x? – 6x – 2 Oy = -…

A: The objective is to find the equation of the graph.

Q: 2) Solve the equation y' = Y 4x²y + x

A:

Q: The parabola shown in the figure has an equation of the form y = ax² + bx + c -5 y 5 (2, 4), -5 -10…

A: The parabola shown in the figure has an equation of the form .The parabola passes through the points…

Q: Find the parabola of the form y=ax^2+b which best fits the points (1,0), (4,4), (6,8) by minimizing…

A:

Q: What is the equation of the parabola that opens to the right and with vertex at (4,-2) and a latus…

A: Prabola

Q: 0/ Find the Palametric equations of the line of intersection of Planes? PL= -2x+3y +7Z =-2…

A:

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

A:

Q: 4) Transform the parabolic equations (9)40xxt120xy けy-20x +0こo x+9 (6) e2x Uxx +2e**Jxy+ e®Uyy=O to…

A:

Q: Standardize the conic with the equation 7x2+4xy+4y2--2x-6y+1=0

A:

Q: If a parabola y=ax2+ky=ax2+k has vertex (0,−1)(0,−1) and passes through the point (4,2)(4,2). What…

A: A Parabola y=ax2+k       ...(1) has Vertex (0,-1) and Passes through the Point (4,2)

Q: Find the directrix of the parabola described by the equation 6 (x – 3) + (y + 2)? = 0 O x = } O x =…

A: The  parabola with vertex at (h,k) and focus at (h-a,k) has a standard equation, (y-k)2=-4a(x-h) The…

Q: The orthogonal trajectory of y = ce* is a parabola of the form y = ax+b. Find the values of a & b so…

A: We are asked to find the value of a and b

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: Find an equation of the parabola with vertex (-5,-4) and directrx y =-11,

A:

Q: The vertices of the ellipse given by = 1 are (2, 1) and (1, 2) (0, 1) and (0, – 1) - O A. В. (-2, 0)…

A: Given:- x2/4+y2/1 = 1 To find:- Vertices of given equation of ellipse

Q: The center of the hyperbola 25x² – y + 150x – 6y+191=0 is %3D A (-3,-3) B (3,-3) (3,3) D (-3,3)

A:

Q: Determines the Cartesian equation of the plan that is parallel to the plan 2x - 3y + z - 1=0 and…

A: We have to find the equation that is parallel to the plane 2x-3y+z-1=0. Also plane passes through…