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 an equation of the Hyperbola that has Foci (-1,–3) & (-1, 7) with asymptotes y = x+ & y = -a+…

A: Standerd equation of hyperboal is (x-h)2a2-(y-k)2b2=1where (h,k ) be the center

Q: What is the general equation of a parabola that opens upward with V(-1,2)?

A: The general equation of the parabola opening upwards is x-h2=4py-k where (h,k) is vertex. here…

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: 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: 3. Find the points of intersection of the parabola ²-4x+y=0 and the line-2x+y=-3

A: Let the co-ordinate of the intersection point be (x, y).  Then (x, y) lies both on the parabola and…

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: Which of the following properties satisfy the parabola with equation x² + 6x + 8y = 7 O v(3,2);…

A:

Q: The hill has the shape of a cone, which in the XYZ system has the equation z = 4 - sqrt(x^2+y^2) A…

A: Given that hill has the shape of the cone given by z=4-x2+y2 and the tourist moves uphill whose path…

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

A:

Q: Find the equation of the hyperbola with vertices (- 3, 2), (5,2) and foci (- 4,2), (6,2) O (x- 2)2…

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

A:

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: The length of the major axis of the cllipse with center (-4, 1), minor axis parallel to the y-axis…

A: Equation of ellipse with center (-4,1) is given by

Q: nd the equation of the parabola with vertex at (5,-2) and focus at (5,-4). (x – 5)² = 8(y + 2) (x +…

A:

Q: Which point on the parabola is one of the roots of the quadratic equation y = -x² – 3r + 4? %3D -2…

A: The roots of the quadratic equation are given by the points at which its graph cuts the x axis.