A 20-in. satellite dish for a television has parabolic cross sections. A coordinate system is chosen so that the vertex of a cross section through the center of the dish is located at (0, 0). The equation of the parabola is modeled by x2 = 25.2y, where x and y are measured in inches. 10 -10 a. Where should the receiver be placed to maximize signal strength? That is, where is the focus? ( b. Determine the equation of the directrix.

Q: b) Consider now the portion of the parabola which is below the line y = 2. Which points have the…

A:

Q: 4. Find the focus, directrix and vertex of the parabola (x + 2)2 = 3y - 6, then sketch the curve.

A:

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: In which direction do the following parabolas open?a. y2 = -4x        b. x2 = 4y

A: Part(a) Given parabola  The graph of the given parabola is

Q: Find the angle at which the parabola y=x2−14 intersects the positive x−axis.

A:

Q: Consider the parabola y = -x +4x + 9 and the line y=2x + 1. Solve for the x-coordinates at their…

A: x - coordinates of the point of intersection = ?

Q: Find the equation of the directrix and the length of the latus rectum of the given parabola.…

A:

Q: Given a parabola's focus at (6, −4) and directrix at y = −7, how would you write its equation?

A: Equation of parabola: x-h2=4py-k Where vertex is (h, k) Focus is (h, k+p) And directrix y = k - p

Q: Find the distance between the point (p, 4p) and the parabola y? = 2px, where p is a fixed positive…

A: let the point on parabola be A= (x, y)  B = (p, 4p) Thus,  AB = x-p2+y-4p2 but parabola is y2=2px…

Q: Where does the line x = 1 + 3t, y = 2−t intersect (a) the x-axis (b) the y-axis (c) the parabola y =…

A: Parametric equations are a set of equations where 2 or more variables are dependent on one single…

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: A] Find the length of the arc of the semi-cubical parabola y2 x (1,1) and (5,5V5). 8250 between the…

A: Solution:Given        y2=x3    between the points (1,1) and (5,55)To find the Arc…

Q: Cоmрute (x + y) dz, where is the portion of the parabola C y = 4 – x2 from -2 to 1+3i.

A:

Q: Find an equation for the parabola that has its vertex at the origin and satisfies the given…

A: Given vertex is (0 , 0) and focus on negative y axis focal diameter is 2

Q: Find the standard form of the equation of the parabola satisfying the given conditions: Focus :…

A: Consider the following values: Focus=9,0Diretrix⇒x+9=0 Standard form of the equation of the…

Q: What is the standard form of the equation of the parabola with the focus (6, –1) and the directrix x…

A:

Q: How far from the y-axis is the center of the curve 2x2 + 2 y² + 10x – 6y – 55 = 0? %3D 2.50

A:

Q: For Exercise, determine the standard form of an equation of the parabola subject to the given…

A: Given directrix: x=0 and focus (-4,5)The vertex will be the mid point of them Mid point of x=0 and…

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

A:

Q: nd an equation for the parabola that has its vertex at the origin and satisfies the given…

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

Q: Find the standard form of the equation of the parabola satisfying the given conditions: Focus :…

A:

Q: for the given audratic equation determine, i- which way the parabolla opens ii- the cordinate of…

A:

Q: find the points on the parabola y=x^2 closest to the point (0,1)

A:

Q: At what point does the normal to y = 3x – (5 + 4x) at (1, –6) intersect the parabola a second time?…

A:

Q: Find an equation of the parabola that satisfies the given conditions.Focus F(2, 0), directrix x = -2

A: If the coordiantes of the focus h+p,k and directrix x=h-p Then, equation of parabola y-k2=4px-h We…

Q: Given the general form of a parabola x2+8x-12y+11=0, what is the equation of the directrix? y=_____.…

A:

Q: How far from the x axis is the focus of the hyperbola (x^2)- (2y^2) + 4x + 4y+ 4 = 0?

A: the given equation of hyperbola is  x2- 2y2+4x+ 4y + 4 =0 it is asked to find how far is focus of…

Q: What is the standard form of the equation of the parabola with the focus (1, –3) and the directrix x…

A:

Q: Find the standard form of the equation of the parabola satisfying the given conditions: Focus : (0,…

A: given, focus (0,15) directrix y=-15

Q: 2. A parabolic antenna has a width across the top of 36 inches and the depth at the center is 6…

A:

Q: For Exercise, an equation of a hyperbola is given. Determine whether the transverse axis is…

A:

Q: d the x-intercepts of the parabola given by the equation. (If an answer does not exist, enter DNE.)…

A:

Q: 8. Show that the circle and the ellipse are tangent to each other and draw the figure, x? + y? – 6x…

A:

Q: Given a focus of (4,5) and a directrix of y=-3, fınd the equation of the parabola. y = (x –

A: We need to find equation of parabola.

Q: 4. Find the equation of the parabola P with focus F = ( 1,1) and the directrix D: x + y = 0 shown in…

A: --------------------------------------------------------------- dQ,F = dQ,DWhere, dQ,F =…

Q: Find an equation of the parabola deseribed. Focus at (5, 0); vertex at (0, 0) O y = 20x2 O x = 20y O…

A:

Q: The filament lightbulb is a thin wire that glows when electricity passes through it. The filament of…

A: Given: The given reflector is 7 inches wide and 2 inches deep i.e. (x,y)=(2,3.5)

Q: Fid the equation of the tanget to the parabola  x2 - 22x + 24y +169 = 0 at  the point whose focus…

A:

Q: The value of y dæ – x dy where C is the portion of the parabola y = x² – 1 from (0, –1) to (-2, 3)…

A:

Q: The points P(ap2 , 2ap) and Q(aq2 , 2aq) lie on the parabola y2= 4ax. Prove that if PQ is a focal…

A:

Q: Find the standard form of the equation of the parabola satisfying the given conditions: Focus : (0,…

A: Given:Focus0,20Directix y=-20Parabola:x-h2=4p y-k

Q: Evaluate x° ds where C is the part of the parabola y = x² from (0,0) to (2, 4).

A: Form the double integral and set the limits than integrate with respect to y and x.

Q: 9.  Find the shorted distance from point A(2, 1/2) to a point on the parabola y = x2. And find the…

A:

Q: The area of the region to the left of the parabola x=2y^2, to the right of the y-axis, and between…

A:

Q: What is the DE of the family of parabolas having their vertices at the origin and their foci on the…

A:

Q: nd the focus, directrix, focal diameter, vertex and axis of mmetry for the parabola 9.96x = y? cus =…

A:

Q: The line x=C where C70 intersects the cubic y= 2x3 + 3x²-9 a七 the point P and parabola y = 4x+ 4x +5…

A:

Q: The signal received by a parabolic antenna is concentrated in its receiver, which is placed,…

A: For the Paraboloid,z-axis is it's Principal Axis,Also, it is symmetric with the lines x = 0 (yz…

Q: Find the standard form of the equation of the parabola satisfying the given conditions: Focus : (2,…

A: Consider trhe focus of the parabola is 2,4 and the directrix is x=-4. Let x,y be any point on the…