1. A parabola having a vertex located at (-4, -8) intercepted the x-axis at x = -2 and x = -6. Determine the length of the arc of this parabola from the intercepted points.

Q: 23. The line 3x - 4y + 14 is a tangent to the circle

A: 23 Given equation of tangent is 3x-4y+14. General equation of circle is x2+y2+2gx+2fy+c=0 radius of…

Q: 3. The towers supporting the cable of a suspension bridge are 1200 m apart and 170 m above the…

A: Solution:-   First we are draw a rough diagram based on the given problem.      Both towers are…

Q: The parabola y = - 16 (X – 2)- -+1 has its fócus at (2, -3). Determine and state the equation of the…

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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: What is the length of the latus rectum of a parabola having its vertex at the origin and focus at…

A: The length of latus rectum of parabola = 4a

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: 25. A parabola is the locus of a point equidistant

A: We know that parabola is locus of the points equidistant from focus (point) and the directrix…

Q: A rectangle is to be inscribed inside a semi-ellipse + = 1, -2 <IS2 and 0 y S 3. Give a rough sketch…

A: Solution is here

Q: Please

A: Now differentiate it with respect to y and equate it to 0.

Q: The area of the triangle formed by the tangent and the normal to the parabola y = 4ax both drawn at…

A: Given  the parabola y² = 4ax both drawn at the same end of the latus rectum and the axis of the…

Q: 3. Write an equation for the parabola with vertex at (2, 3), opening upward, and with no vertical…

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Q: 7, All circles of radius 5, with their centres on the y-axis. 8. All parabolas with x-axis as the…

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Q: 2. Parabola with x+1= 0 as the directrix, y = 1 as the axis, and the length of the latus rectum is…

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

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: A point moves on the parabola 10y = 5x² + 3 in such a way that when x = 6, the abscissa is…

A: Given: A point moves on the parabola 10y=5x2+3, when x=6 the abscissa is increasing at the rate of 2…

Q: 7. Find the equation of the circle with center (2, -4) and tangent to the y- axis.

A: As per guidelines we are supposed to solve the maximum one questions at a time. plz repost another…

Q: 1.) A gateway is a parabolic shape whose vertex is 20 ft. From the ground, (0,20), and the width of…

A: Given, a gateway  is a parabolic shape whose vertex  is 20 ft. From the ground, (0, 20), and the…

Q: A parabola has its axis parallel to the x-axis, one end of its latus rectum at (-15/4,3/2) and…

A: Given Information:A parabola has axis parallel to the x-axis.Latus rectum at -154 , 32Vertex at (-1,…

Q: 5. The equation of a family of parabolas with axis paralel to the y-axis is

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Q: 9) Find the point on the parabola y = 10-x² closest to the point (0, 5.5).

A: Given question:- Find the point on parabola y= 10-x2 closest to point (0,5.5)

Q: Find the shortest distance from the point (1,4) to a point on the parabola y =2 x (a) /2 (b) 1 (c) 2…

A: To determine the shortest distance between point and the parabola,

Q: 1. Find the center and radius of circle x2 + y--2x-4y+1= 0.

A: 1) To find the center and radius of circle x²+y²-2x-4y+1=0

Q: Find the length of the arc of the semicubical parabola x  sq = ycu . betweenthe points (2,2 )  ; (4,…

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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: If the coordinates of the ends of a focal chord of the parabola y²=4ax and (x,,y,) and (x,.y;) then…

A: Consider the given parabola y2=4ax Suppose Ax1 , y1  and  Bx2 , y2 be the ends of the focal chord of…

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: 1P If an automobile head light reflector is cut by a plane through its axis, the section is a…

A: Given : Diamete of the headlight is 250 mm.

Q: Find the tangent line to the parabola x2-6y=10 through (3,5) (ILLUSTRATE SOLUTION)

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Q: Find the shortest distance +rom the point (0,5)to the ellipse 3 y? = x'

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Q: Determine the value(s) of k such that the circle x²+(y-6)²=36 and the parabola x²=4ky will intersect…

A: Consider the provided equations, x2+y-62=36  ....... (1) x2=4ky ...... (2) Determine the value(s) of…

Q: Given the parabola x^2=4y, a line passes through point A (4,4) and the focus of the parabola. Find…

A: Topic:- Parabola

Q: From any point (N) on a hyperbola, the combined distances to the foci (f1 and f2) is equal to what?

A: A hyperbola is two curves that are like infinite bows. Looking at just one of the curves: any point…

Q: A parabola with a negative latus rectum has endpoints at (5, 1) and (5, -11) Where is the vertex? *

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Q: Given the point P =,(a,b) in the first quadrant, find the downward-opening parabola that passes…

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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: Determine the coordinates of points A and B on a parabola y midpoint of AB is as close as possible…

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Q: Find the minimum distance between the point (5,1) and the parabola y=-x2 ?.

A: Find the minimum distance between the point (5, 1) and the parabola y = -x2?

Q: [1] What is the c value of a parabola with a Vertex of (4,2) and a Focus of (4,4)?

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: Find the equation of Parabola and Graph with the following information: Center at (0, 0) Vertices…

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Q: Find the length of the latus rectum of the parabola x2 = 4py. Then find the length of the parabolic…

A: Given , Equation of parabola  x2 = 4py     Comparing with the Standard Equation of Parabola  x2=4ay…

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

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Q: Show that the envelope of the family of circles whose diameters are the double ordinates of the…

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Q: 1. Which of the following best describes the graph of y = x? – 4x + 2? a parabola with a vertex at…

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Q: Is the graph of x2 + y2 = 0 a circle? If so, what is the length of a radius?

A: The standard form of the equation of the circle is (x-h)2+(y-k)2=r2. Here (h,k) is the center and r…

Q: Plot both the following curves on the same set of axes. r = 5 − 4cos(θ), and the parabola y = x².

A: We have to Plot both curves on the same set of axes. r = 5 − 4cos(θ), and the parabola y = x².

Q: If P(a, a²) is any point on the parabola y = x², except for the origin, let Q be the point where the…

A: To Determine: If P(a,a2)is any point on the parabola y=x2,except for the origin,let Q be the point…

Q: 2. Find the equation (in general form) of the tangent lines to the circle x² + y² - 8x + 10y = 128…

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Q: =+ dr x = 2 ke x = 3 16 2x2

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Q: 8. Find the equation of the circle with center (-9, -3) and tangent to the x- axis.

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