5(c) Find the rectangle with the largest area that can be inscribed in the top half of the ellipse ² + 4y2 = 1; that is find the (x, y) coordinates of the top corner in the first quadrant of the rectangle below that has the largest possible area: 1 y=√1-x² (x, y) -1 1

Q: Find the length of latus rectum of the ellipse 36x2 +25v²+72x-50y-839 = 0: Round off your answer to…

A: The given ellipse equation is 36x2+25y2+72x-50y-839=0. First write the equation in standard form as…

Q: Find the equation for the parabola that has its focus at the (- 5 4 For the toolbar, press ALT+F10…

A: Given:The focus of the parabola is located at .The directrix is a vertical line with the equation…

Q: A comet’s path (as it approaches the sun) can be modeled by one branch of the hyperbola [(Y2 ) /…

A:

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 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: Explain why : exponential equations of the form y= a x 2 ^(b(x-h)) + k have no roots if: a) a0 and…

A: The given exponential equation is

Q: Find the equation of the hyperbola with vertex (-4, 0) and foci at (-5, 0) and (1, 0).

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

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: 7. For the parabola 4x + 2y² + 8 = 0, fine the directrix. (a) y = x = (C) 3 N|WN| W | 2 (b) (d) x =…

A: Given query is to find the directrix of the parabola.

Q: Show that the number 4p is the width of the parabola x2 = 4py (p>0) at the focus by showing that…

A:

Q: x² y²=1? What is the area of the ellipse: + 36 16

A: For the calculation of area of ellipse,

Q: The family of parabolas y =(1/a )-(x2/a3) ,where a > 0, has the property that for x ≥ 0, the…

A: Given, Equation of parabola y=1a-x2a3 where a>0  and x≥0 x-intercept is (a,0) y-intercept is 0,1a

Q: Find the equation for the parabola that has its focus at the (−7/4,−9) and has directrix at x=15/4

A: Here we have to find equation of parabola with given focus and directrix.

Q: 1. Sketch the quadratic y=x²-3x+2. Find the vertex of the parabola Enter your answer in the form:…

A:

Q: The parabola passes through the points (−3/2, – 1), (1, 5) and vertex is at (0, 4) with a horizontal…

A:

Q: A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola y = 4 –-…

A:

Q: 4) Consider the images of the hyperbolas r - y = ±c? under the mapping f(2) = 22, where c > 0. Show…

A:

Q: The center of the ellipse with the given equation 4(x – 5)² + 3(y – 4)2 = 48 is %3D (-5, 4) (4, 5) O…

A: Solving the problem by finding the centre in standard form.

Q: Find the values of integers,, and c that will make the hyperbola -9x² + 4y² + ax +by+c= 0 pass…

A: