Show that the envelope of the family of circles whose diameters are the double ordinates of the parabola y = 4ax is the parabola y = 4a (x + a). 7. Fin- %3D Pro

Q: A rectangle has its base on the x-axis and its upper two vertices on the parabola y = 4 – x². What…

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Q: Farmer Jones and his wife, Dr. Jones, decide to build a fence on their farm. Because Dr. Jones is a…

A: Follow the procedure given below.

Q: dr if F= and C is a piece of the parabola y=4-x² from the point (–1,3) to the point (2,0).

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Q: Sketch the graph of the circle or semicircle.

A: Here we have to Sketch the graph of the circle or semicircle. The given equation is  9x2+9y2=1

Q: A rectangle is inscribed in a parabola y^2 = 16x with the side of the rectangle along the latus…

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Q: Let P and Q be distinct points on the parabola y = 2r such that a circle with PQ as diameter passes…

A: The given equation of parabola y2=2x Let P and Q be points on the parabola  Parametric coordinates…

Q: Which point is the center of the circle* 4x2 + 4y2 = 4y - 8x + 5? %3D

A: Given that: 4x2+4y2=4y-8x+5

Q: 6.Find the area for a circle that has a radius of 4x3y3

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Q: 2. Circle the parabolas that are stretches of the graph y = x². а) у3 1.25х? c) y = – x? b) y = 0.25…

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Q: Show that the center of the osculating circle for the parabola y = x2 at the point (a, a2) is…

A: We need to show that the centre of the osculating circle for the parabola y = x2 at the point (a,…

Q: 2=2X Find the point that is close' to the pont'(,4) on the parabola y

A: Explained below

Q: What is the radius of the circle defined by x² + y? – 4x + 6y = 7

A: Given,           x2+y2-4x+6y=7To find : The radius of the circle.We know that,          The standard…

Q: Which point is the center of the circle 4x² + 4y2 = 4y – 8x +5 ?

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Q: Name and graph the following quadratic surface. 9x2 + 4z2 – 36y = 0

A: For (b) Sketch of z=9-x2-y2: The graph is a paraboloid.

Q: 5. Determine the value(s) of k such that the circle x² + (y – 6)² = 36 and the parabola r? = 4ky…

A: we have to find the value of k. the solution is following.

Q: Q13:- Given a parabola y? P1 tangent to the parabola. Find the area of the triangle A0AB = 4px, and…

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Q: 19. Find the total area between the parabola y = x2 - 4x, the x-axis, and the ordinates x = -2 and x…

A: We can use integration to calculate the area

Q: Find the dimensions of the reclanyie uf iurg lying on the parabola. y = 6- x2 width units height…

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Q: What is the directrix of the parabola? (x – 4)? = 8 (y + 3) O x = -3 O y = -3 y = -5 x = -5

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Q: The points of intersection of the graphs of xy = 20 and x² + y? = 41 are joined to form a rectangle.…

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Q: Graph the dilated image of Quadrilateral ABCD using a scale factor of ½ and center of dilation (1,…

A: We measure the distance between center to all points and scale by 2 to get the dilation…

Q: enclosed betw parabola y = x2

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

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Q: Find the point on the parabola y = (x – 3)² – 5 that is closest to the point (0,0). |

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Q: 4 SKetch the parabola and label the foces , ventees and dineder 2. 4 -6y -2utl=0

A: To find- Vertex, focus and directrix of a given parabola.

Q: In te ypane, the gaph of the eqation x*+4y + 4x + 24y + 24 = 0 is a circle O an ellipse O an…

A: The solution is given as

Q: 2. Consider the equation r = 4 – y². (a) Find a parameterization of the segment of this parabola…

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

A: Let (x,y) = (x,x2) point on the parabola is closest to A Distance between (2 , 1/2) and (x,x2) is:…

Q: 2. Sketch the graph of the cylinder given by 4x? + 9y² = 36.

A: Graph of the cylinder. You can assume that the the elliptical like shape is above the given figure…

Q: if the point (a, b) is on the parabola y=6x^2-(5785/12) that is closest to the point (0,4) than a ?

A: Given, y=6x2-578512 suppose x,y any point closest to 0,4  D=x-02+y-42 put y in equation,…

Q: 4. Fit a second degree parabola y = a + bx + cx? to the following data 2. 8. 10 y 3.07 12.85 31.47…

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Q: Find the center and radius of the circle.x2+y2−10x−6x =−9

A: We will write the equation in standard form first. For that, we have to complete the square. We…

Q: Find the radius of the circle 2x 2+2y 2=50

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Q: 13. Find the point on the parabola y* = 2x that is nearest the point (1, 4). %3D

A: As per our guidelines we can solve only one question or three sub-parts. To ask more please…

Q: A rectangle has its base on the x-axis and its upper two vertices on the parabola y=6-x² What is the…

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Q: Find the point on the parabola y 2 =2x that is closest to the  point ( 1, 4)

A: Given: y2=2x let's point on parabola is t22,t now, if point1,4 is closest to t22,t2 then product of…

Q: What is the largest possible area of a rectangle inscribed in the region bounded by the parabola y =…

A: According to the figure, we have

Q: A rectangle is inscribed with its base on the ?x-axis and its upper corners on the parabola y=2−x^2.…

A: Given, The equation of the parabola is y=2-x2

Q: What are the points of intersection between the graphs of the circle and parabola? x² + y? = 37 x² =…

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Q: How long is the latus rectum of the parabola y? + 3x – 12 = 0? O 12 6. 3. 3/4

A: Converting the equation to standard form

Q: Find the point on the parabola y=x2 closest to (6,3

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Q: Find the area of the largest rectangle that can be inscribed in the ellipse given by: x² + 4y? = 16

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Q: Find c > 0 such that the area of the region enclosed by the parabolas y = x^2 - c^2 and y = c^2 -x^2…

A: Given parabolas, y=x2-c2y=c2-x2

Q: 6. KAWE is an isosceles trapezoid with midsegment LS. Determine the length of LS. 2 6 2x W. 4x-4

A: Given, KAWE is a isosceles trapezoid which means that it has congruent diagonals. We need to…

Q: True or False The radius of the circle x2 + y2 = 9 is 3.

A: Given equation of circle is: x2+y2=9 Then we get, x-02+y-02=32

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

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Q: 2. Find the point on the parabola x+y? 0 that is the closest to the point (0, -3).

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Q: Find the shortest distance of the point (6,3) to the parabola y=x2

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Q: 3. What is the radius of the circle passing through the vertex and endpoints of the latus rectum of…

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