Find the points of intersection of the parabola with equation 2x + y² + 4y – 2 = 0 and the line passing through the point (-3, –4) with y-intercept -1.

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: 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 the equation of the parabola, y = ax^2 + bx + c, that passes through the points (0,5), (2,-5),…

A: we have to find the equation of the parabola y=ax2+bx+c that passes through the points (0,5), (2,-5)…

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: 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 point(s) of intersection of the line y=7x-42 and the circle with equation x2+y2-4x+6y=12.

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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: 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 indicated half of the parabola.Left half of (x + 3)2 = y + 2

A: We have the given equation of parabola   the equation is (x + 3)2 = y + 2   we have to find the…

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 slope of the ellipse x2 + 4y2 -10x - 16y +5=0 at the point where y=2 + 80.5 and x=7

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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 the equation y=ax^2+bx+c of the parabola that passes through the points (-2, 0), (0, -14), (7,…

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Q: Find the equation of the parabola, y=ax^2 + bx + c, that passes through the points (1,4), (-1,0),…

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Q: Graph the equation 3x - 4y = 8 on the xy-plane

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Q: Consider the graph of  y = ax2 + bx + c, where a = -3, b = 2 and c = 1.  Is the parabola concave up…

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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: The parabola y2 =-14x has it's focus at the point (b,0) where b is?

A: The standard equation of parabola for this condition is y2=-4ax here  Focus (-a, 0)   Now, we have…

Q: Find the equations of two lines through the origin that are tangent to the ellipse 2x - 6x+y +4 = 0

A: Consider the given equation:2x2−6x+y2+4=0Let a line y=mx+c is a tangent to the ellipse.Tangent…

Q: Find the standard form for the equation of the line which passes through the point (2,0) and which…

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Q: Find the equation that is perpendicular to y = x +3 and passes through the point (-3, -4). %3D Oy =…

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Q: Find the equation of the line perpendicular to 8x + 2y = 1 passing through the point (4, Y = -X

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Q: The equation of the parabola that has a vertical axis of symmetry, touches the line y= 6 and has its…

A: Your 3rd option is your correct option...detailed solution I have done step by step in…

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

A: Here we find the equation of parabola.

Q: Find the x intercepts of the parabola y=x^2-7

A: Given: y=x2-7                                              ..1 we know that at x-axis, y coordinate…

Q: Find the points of intersection between the line 4y - 3x + 12 = 0 and the ellipse 9x 2 + 16y 2 =…

A: The line 4y-3x+12=0 And the Ellipse 9x2+16y2=144 We need to find the intersection point of the line…

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

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

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Q: Graph the curves and show that the 2x2-y2=C is a solution to yy'-2x=0.

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Q: Determine the points of intersection of the parabola y=2x^2 +12x +10 and the line y=4x+2

A: I am attaching image so that you understand each and every step.

Q: (3) Find the coordinates of the points of intersection of the parabola y = x2 - ax and the line y =…

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Q: Sketch the parabola and line on the same graph. y = x2 + 4 and y = 2x + 2

A: Given, y=x2+4   y=2x+2  The graph of given functions can be plotted as shown in the figure below.

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: If the parabola whose equation is x = ay2 + by + c has its vertex at (3,2) and a&gt; 0, then it has…

A: The given statement is that" if a parabola whose equation is x=ay2+by+c has its vertex at 3,2 then…

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: Assume the equation of a parabola and a line are given by y = x +2 x and y =3 x +6, respectively.…

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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 of the parabola that is symmetric about y axis with vertex at the origin and…

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

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

Q: Find the equation for the hyperbola that asymptottes (y - 3) = +- 1/square root of 2 * (x+3) and…

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Q: Find the equation of the parabola y = ax^2 + bx +c that passes through the points (-1,-4) (1,4), and…

A: topic  -  parabola

Q: Find the equation of the line tangent to (a) The parabola z = 2x² - 3y², y = 1 at the point (-2,1,5)…

A: Given: we have to find equation of tangent lines   equation of tangent line : y-y1=m(x-x1)

Q: Determine the coefficients a, b, and c of the parabola y = ax² + bx +c that passes through the point…

A: Solution is here