0. Let E be the region inside the ellipse 4x² +9y² = 36 and above the X-axis. Find the average Y coordinate of a point in this region.

Q: he area of an ellipse with axes of length 2a and 2b is nab. The percent change in the area when a…

A: We have to find percent change in the area after increasing major axis and minor axis.

Q: Find the perimeter of the ellipse x2/a2 +y2/b2 = 1, where a > b > 0.

A: The perimeter of Ellipse with Radii a and b is given by: In our question the radii is a and b Hence…

Q: Find a normal of slope 2/3 to the hyperbola 3x2-4y2=8

A:

Q: A. Solve for u : 3 u₂ x + Ux = 3u, u(1, y) = In(y) U = B. Find the critical points (xe, yc) of the…

A:

Q: 3. Find the line normal to the ellipse at X=-1 y= 2+4x-x3

A: Given, y=2+4x-x3 At x= -1 y=2+4-1--13y=2-4+1y=-1 Now point -1,-1

Q: Find the minimum distance from the point (4,2) to the parabola y2 = 8x.

A: We have to find the minimum distance from the point (4,2) to the parabola y2=8x.

Q: Find the points on the ellipse  (x2/9) + y2 = 1 closest to the point (2, 0).

A:

Q: 3. Use calculus (derivative and C.N.) to find the area of the largest rectangle that can be…

A: This question is related to conic section .solve in step 2.

Q: What is the area of the ellipse x² 16 + y² 9 = 1?

A:

Q: Find the envelope of the family of ellipses x2a2+y2b2=1 having the same area.

A:

Q: 2. Which equation represents a parabola with vertex (4,4) and directrix y = 2? Oy=2x² - 4x + 4…

A:

Q: Consider the ellipse x^2 + 2xy + 4y^2 = 12. a. Find the two points on the ellipse with x…

A:

Q: Find the area of the largest rectangle that can be inscribed in the ellipse  x2/a2 + y2/b2 = 1.

A: Let (x,y) be a vertex of rectangle. Then, length of rectangle = 2x, width = 2y. Then area of…