2 1.² + a² 6² 1² Find the area enclosed by the ellipse x² that the area common to ellipse a² b² 2 auxiliary circle x² + y² = a² is equal to the area of another ellipse whose semi axes are a and a - b. = 1. Also prove x. =1, a> b and its

Q: 3. Find the coordinates of the foci of the ellipse given by the equation 4x² + y? = 64. O (0, 4v3)…

A:

Q: Calculate the standard for eq of the ellipse Foci (3,2) and (3,-4) L of Major axis = 10

A:

Q: Given the values ​​of a = 4, b = 3, determine the equation of the vertical ellipse.

A:

Q: O Does the origin lie inside or outside the ellipse with equation (x – 4) 2 + 4(y - 3) 2 = 4?

A:

Q: Consider the point P(−1,0) on the ellipse 4x2+y2=4. There are two points (a,b) and (a,c) on the…

A: We will find the value of a as following.

Q: A rectangle is to be inscribed inside a semi-ellipse + = 1, -2 <IS2 and 0 y S 3. Give a rough sketch…

A: Solution is here

Q: (x-1)^2/81 + (x+2)^2/36 =1 parametrize the ellipse and include the interval for t

A: See the pic

Q: A hyperbola in standard position has equation 36x2 −49y2 −100 = 0. Write down a parametrisation of…

A: The given equation of the hyperbola is: 36x2-49y2-100=0 Rewrite the equation:…

Q: Consider the point P (-1,0)on the ellipse 4x2 + y? What is the value of a? Answer to 3 significant…

A:

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: Le area of the ellip А. 15п sq. . 25п sq. ur sq. un В.

A:

Q: 5. Sketch the parabolas showing the intercept and the maximum/minimum points. a) y = 2x – 4x +7 b)…

A:

Q: . If the line 3x+4y=\sqrt{7 } touches the ellipse 3x\power{2}+4y\power{2}=1, then find the point…

A: a.Let the given line touches the ellipse at point P(θ).The equation of the tangent at P is…

Q: What is the equation of an ellipse having vertices at and a minor axis (0,+8,) which is 6 units in…

A: the standard equation of the vertical ellipse is given by x-h2a2+y-k2b2=1

Q: 26. Find the standard form of the equation of the specified ellipse. Foci: (1, 5), (-3, 5); Major…

A:

Q: Match the ellipsoids shown in the table with the equations. Answer Bank x2 + 2y2 + 2z² = 4 2x2 + 2y?…

A:

Q: 10. Show that the ellipse and hyperbola, */*+2=1, 3 intersect at right angles.

A:

Q: Which of the following is the standard equation of the ellipse with vertices at (1, 0) and (27, 0)…

A:

Q: Find the extreme values of the function subject to the given constraint. f(x, y, z) = (x - 1)2 +…

A: As per company guidelines we are allowed to solve one equation at a time so i am solving first one…

Q: Show that the ellipse x*/a? + y*/b? = 1 and the hyperbola x/A? – y/B² = 1 are orthogonal…

A:

Q: 10.46.) A satellite orbits the planet Neptune in an elliptical orbit with the center of the planet…

A: Solve for the maximum distance between the satellite and the centre of the planet

Q: The plane x + y + 2z = 2 intersects the paraboloid z = x² + y² in an ellipse. What is the point on…

A: We will use Lagranges multiplier method to find optimal solution  To maximize/ minimize f(x,y,z)…

Q: What is the length of latus rectum of the ellipse given the equation, 81(r + 8) +144(y- 2) = 11664?…

A: We need to find length of latus ractum of ellipse.

Q: Find the maximum area of an isosceles triangle inscribed inside the ellipse x²y² 1, + = a² 62 with…

A: Given problem:- Find the maximum area of an isosceles triangle inscribed inside the ellipse x2/a2…

Q: What will be the equation of the ellipse with a center at the origin and passes through the points…

A: Given query is to find the equation of ellipse.

Q: 28. Find the directrix for the parabola. (y+ 3)2 + 8 2x x = 4 y = } 7/2

A: