find the general equation of the parabola with horizontal axis which crosses the x-axis at x=2 and the y-axis at y=-1 and y=7

Q: Find the parabola with equation y=x^2+bx+c that has slope of 8 when x=9 and passes through the…

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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: Which of the following equations is the equation of tangent to the parabola y2 = 2x + 8 at point…

A: The given equation of parabola is: y2=2x+8

Q: Find the coordinates of the vertex of the parabola y = x^2 - 4x + 1 using derivatives O (2, -3) O…

A: To find the vertex of the parabola by using derivatives

Q: Find a parabola with equation y = ax2 + bx + c that has slope 8 at x = 1, slope −12 at x = −1, and…

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Q: Determine the general equation of a parabola opening downwards whose vertex is at (3,-4) with a…

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Q: Find the point on the parabola x= - 2t, y = - 2t, - o <t< oo, closest to the point (- 32, – 1).

A: Let the point (x, y)=(-2t, -2t2) on the parabola be the closest point to (-32, -1) So distance…

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

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Q: Find the equation of the line tangent to the hyperbola x + 2xy - y + x = 5 at the point (3,7)

A: Given,            x2+2xy -y2+x =5 and point (3,7)

Q: How can we find the slope of the parabola y?

A: You can’t find the slope of the parabola y , because a parabola is not a line. You can find the…

Q: Find a parabola with equation  y = ax2 + bx + c  that has slope  13  at x = 1, slope  −19  at x =…

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

A: equation of parabola:-

Q: Find an equation for the curve traced by the point P(x, y) if the distance from P to the vertex of…

A: First find the vertex and focus of x^2=4y

Q: In the xy-plane, a line that has the equation y = c for some constant c intersects a parabola at…

A: in the xy-plane a line that has the equation y=c for some constant c intersects a parabola at…

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

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

A: Given:Vertex=0,0Directrix y=-3Equation of parabola:x-h2=4py-k

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

A: First we have to calculate distance from directix to vertex. I.e P Then insert values of center and…

Q: Find the general equation of the parabola with vertex at the origin and focus at (-4, 0)

A: The general equation of a parabola with vertex (h,k) is (y-k)2=4a(x-h)

Q: 2. What is the value of y anytime a parabola intersects the x-axis?

A: It is known that the value of y on x-axis is always 0.

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

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

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Q: Find the equation for the parabola that has its vertex at the 1 origin and has directrix at y 41…

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Q: Find b and c so that the parabola with equation y = 4x2 - bx - c has a vertex at (2 , 4)?

A: Using the vertex formula we find the x value of the vertex[formula: x value of vertex of Ax^2+Bx+C=0…

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

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

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

A: It is given that the Vertex is V(0, 0) The focus is on the positive x axis, 2 units away from the…

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

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Q: Find the coordinates of the point on the parabola y = x² which is closest to the point (3, 0).

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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 a parabola with equation y= ax2 + bx +c that hasslope 4 at x=1  , slope -8 at x= -1 , and…

A: The parabola is y=ax2+bx+c. It has a slope of 4 at x=1 and slope of -8 at x=-1 and passes through…

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 the point on the parabola y = x³ that is closest to the point (1, 2) with two digits accuracy…

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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: 5. Find the equation of the hyperbola whose asymptotes are the straight lines x = 0 and y = 0 and…

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Q: The parabola y = x² is shifted up by 7 units and to the left by 1 unit. What is the equation of the…

A: Equation of parabola is given as y=x2. If the parabola is shifted by a units and to the left by b…

Q: 1. For the parabola equation: (y-2) = -3(x+4)^2 + 7, in which direction does the parabola open? *

A: We have to find the direction in which the given parabola opens.

Q: Find the point(s) of intersection of the parabola with equation y = x2 - 5x + 4 and the line with…

A: Given equations are,

Q: 2. Write the general equation of the parabola with directrix at x FG,-1), and v (. -1). 2

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Q: Find the y-intercept and any x-intercept(s) of the parabola with equation y = -(x + 7) + 16. If the…

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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 = x2/2) that is closest to the point (-4,1)

A: Use distance formula to evaluate

Q: The equation of the line touching both the parabolas y = 4x and x' =-32y is x-2y+1 = 0, then a is

A: Introduction :

Q: - Find a parabola with equation y = ax? + bx +c that has slope 4 at x = 1, slope –8 at x = -1, and…

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Q: 4. Find the equation of a parabola with axis parallel to the y-axis and passing through ( ). G. 3…

A: According to our guidelines, In case of multiple questions we are supposed to answer the first…

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: What is the equation of the parabola with a vertex at (4.8) and a directrix at y = 53

A: This is a simple question based on conic section (Topic is parabola) before attempting this question…

Q: Find a parabola with equation y=ax^2+bx+c that has slope 4 at x = 1, slope -8 at x = -1, and passes…

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Q: Find the equation for the parabola that has its vertex at the origin and has directrix atI = 27…

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Q: Suppose the axis of a parabola is parallel to the yy-axis and passing through the points (0,3),…

A: Given that, the axis of a parabola is parallel to the y-axis. Let the Vertex of the parabola (h, k)…

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

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