Find an equation of the paranola in standard form: with the vertex at V (2,-4) and directrix y= -5

Q: Find the standard equation of the parabola with directrix x + 1 = 0, axis y = 1 and the length of…

A: If the axis of parabola is y = 1, then the parabola is horizontal. As we know that the standard…

Q: Find the equation in rectangular coordinates of the quadric surfaceconsisting of the two cones φ =…

A: The relation between spherical and rectangular coordinates in polar form is given by the following…

Q: Use the Distance Formula to write an equation of the parabola with focus F (0, – 11) and directrix y…

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Q: Find the standard equation of the parabola which satisfies the given condition. Focus (7, 11),…

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

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Q: Given a focus of (2, 4) and a directrix of y= -2, find the equation for the parabola. (2-

A: Given:    focus (2 , 4)    directrix y = -2

Q: Find the equation of the parabola with directrix x + 1 = 0, axis y = 2, and latus rectum 3. (two…

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Q: In which direction does the parabola x = -y 2 + 3 open?

A: x=-y2+3 There are two patterns for a parabola, as it can be either vertical (opens up or down) or…

Q: determine the points that are symmetric with respect to (a) the x axis, (b) the y axis, and (c) the…

A: Determine the points that are symmetric with respect to (a) the x axis, (b) the y axis, and (c) the…

Q: The parabola y=x^2+13 has it's focus at the point (b,c) where  b= c=

A: The given equation of the parabola is, y = x2+13. Also the parabola has its focus at (b, c).Consider…

Q: Find the coordinates of the points that are 13 units away from the origin and have an x-coordinate…

A: Solution: Find the coordinates of the points that are 13 units away from the origin and have an…

Q: Determine the type of conics for each equation using the discriminant. 24. 4x2+y2 +24x-4y+36 = 0 25.…

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Q: find center verticals, foci and sketch its graph 2x2+3xy-4y2-3y+1=0

A: We are given : 2x2+3xy-4y2-3y+1=0 Plotting the graph, we have : This graph is a Hyperbola.

Q: Find equations for two lines through the origin that are tangent to the ellipse a- 8x +y + 3 =0.

A: We are asked to find the equation of two lines that are tangent to the ellipse.

Q: Find the equation of the parabola with directrix y = 3, axis x = 0, and latus rectum 4. (two answers…

A: The standard equation of the parabola is (y-k)=4a(x-h)2, where h and k are the coordinates of the…

Q: Find the equation of the plane perpendicular to the y-axis and passing through the point (3,2,-2)

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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 coordinates of the other endpoint of the segment, given its midpoint and one endpoint.…

A: Let A and B are two endpoints of the segment AB. The coordinate of midpoint M is given by the…

Q: Determine the equation of the parabola using the given information. Focus (0, −3) and directix y =…

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Q: Find an equation of the parabola in standard form: with focus at F(7,-1) and directrix 6 units from…

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

A: We have Vertex=(0,0)Directrix x=-15

Q: Find the equation of the parabola with directrix x + 1 = 0, axis y = 2, and latus rectum 3. (two…

A: The equation of directrix of the parabola is x+1=0. The length of the latus rectum is 3. The…

Q: Find equations for the osculating circles of the parabola y=0.5x2 at the points (0,0) and (-1,1/2).

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Q: Find the coordinates of the other endpoint of the segment, given its midpoint and one endpoint.…

A: Given, Midpoint of segment =7,-1  endpoint of segment = 6, 8   We have to find the other endpoint of…

Q: Use the Distance Formula to show that the equation of the parabola with focus F(0, 1) and directrix…

A: Given that Focus of the parabola is F0, 1 and Directrix is y=-1 We have to prove that y=14x2 is the…

Q: (b) Find a rectangular-coordinate equation for the curve by eliminating the parameter.

A: Given equations in the parametric form as:x= cos2(t), ............................(1)y = sin2(t)…

Q: Find all points having a y-coordinate of -6 whose distance from the point(1,2) is 17. (a) By using…

A: Equation relates the number of variables combined together by algebraic entities using equality…

Q: Sketch parabola y = x2 – 10x + 16 by plotting a few points to left and right of the vertex. (Find…

A: Given parabola y=x2-10x+16                  ....(1)

Q: Graph the two parabolas y = x2 and y = −x2 + 2x − 5 in the same coordinate plane. Find equations of…

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Q: Find the point (x, y) on the ellipse, 4(x - 1)^2+ y^2 = 1, that is farthest to the origin (0, 0).

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Q: Find the coordinates of the points of intersection of the parabola y = x2 and y = x+3.

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Q: Find the point(s) on the parabola x =y closest to the point (0,3)

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Q: Find the point on the parabola * +y“ that is closest to the point (0, -3). =

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Q: the center-radius of the equationn 9x²-18 x+ 9+9y? + 12y=12 be obtained by adding both sides of the…

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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 equations for two lines through the origin that are tangent to the ellipse x - 8x + y² + 5 = 0.

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

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Q: Determine the type of conics for each equation using the discriminant. 20. 5x2 + 2x + 3y - 5 = 0 21.…

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Q: At what points will the line y =x intersect the unit circle x2 +y2 =1 ?

A: We have to find the points where line y=x is intersecting the unit circle: x2+y2=1 To find the…

Q: Find the vertices and foci of the ellipse: 6. (x-1) (y+3)? = 1. Round to nearest tenth if…

A: Given- x-129+y+3236=1 To Find- The vertices and focii of the ellipse.

Q: which satisfies th

A: Parabola: The focus of the parabola is (-2,-5) The directrix x=6 The general form of parabola is…

Q: Determine the type of conics for each equation using the discriminant. 27. y2-x-10y -3 0 28. x2-2y2…

A: Solution is given below:

Q: Find the point P on the parabola y = x2 closest to the point (57, 0). (х, у) %3D ]-«

A: Given the equation of parabolay=x2         ........(1)

Q: find the orthogonal trajectory of family of parabolas represented by the equation…

A: To find orthogonal trajectories of  y2=4ax.

Q: Find the standard form of the equation of the parabola satisfying the given conditions. Foci: (2,4)…

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Q: What will be the equation of hyperbola that satisfies the given condition foci at (+ 24,0) and the…

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Q: Find the parabola with equation y = ax? + bx whose tangent line at (2, 8), is y = -2x + 12.

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Q: find a cartesian equation for the curve r=3cos(θ)

A: Cartesian equation for the curve is r=3 cos(θ)   Now x=r cos(θ)  …….. equation(1) cosθ=xrr=3xcosθ…

Q: Find the standard form of the equation of the circle. Center ( - 1, 3) and tangent to the line y = 2

A: To find: The standard form of the equation of the circle. Given information: Center ( - 1, 3) and…

Q: Find an equation of the parabola that satisfies the given conditions.Focus F(0, -4), directrix y = 4

A: To find: The equation of the parabola that satisfies the given conditions. Given information: Focus…