Consider the ellipse with equation x2/ 4 + y2/ 9 = 1. The points of this ellipse where the curvature is maximum are:   a. (2,0)(2,0) and (0,3)(0,3) b. (2,0)(2,0) and (−2,0)(−2,0) c. (0,3)(0,3) and (0,−3)(0,−3) d. (0,3)(0,3) and (−2,0)

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

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Q: Consider the ellipse 25x² + 49y² = 1225. Consider the point P(14,5). Find an equation for both lines…

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Q: What is the equation of a parabola with focus at (2,6) and directrixx = 8? %3D O y - 12y + 12z – 24…

A: Equating distance from directrix to distance from focus gives equation of parabola.

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

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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: Show that line d:3x-4y-5=0 is tangent to hyperbola H:x2-4y2=5 and find the point of contact of the…

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Q: Write the equation of the sphere with centre at ( 0,0,0) and radius = 2

A: The center of the sphere is:(h, k, j)=(0, 0, 0)The radius of the sphere is:r=2

Q: Find an equation of the line in parametric form that passes through the vertex of the paraboloid…

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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: The paraboloid z = 8-x-x²-3y2 intersects the plane x = 2 in a parabola. Find parametric equations in…

A: The equation of the paraboloid is given as z=8-x-x2-3y2. The paraboloid intersects the plane x=2 in…

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: determine the equation  of the conic of foci (1,-2) and (5,-2), and eccentricity e=2/3

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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: Identify the focus and directrix of the parabola: y = -4(x - 2)² - 3. f: (1, -4), d: y = 2 f: (2,…

A: If the equation of parabola is of the form x-h2=4py-k(i)  if p>0  then focus is h,k+p  and…