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

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 equation of the line tangent to the ellipse x + 3y 19 at the point (4,1). (Type an…

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Q: At what point does the line normal to the graph of y=5−4x+4x2 at (1,5) intersect the parabola a…

A: The given function is- y=5-4x+4x2.................1 Differentiating the above expression w.r.t. x-…

Q: An ellipse has the equation 16x² + 25y = 40O. Determine the equation of the tangent of the curve at…

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Q: Find the equations of both the tangent lines to the ellipse x^2 +3y^2 = 9 that passes through the…

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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 the standard equation of the parabola with x intercepts at x = 2 and x -3, and a y-intercept at…

A: Solution is given below

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 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: Find the equation of parabola “y = ax2 + bx + c” passing through points (1, -6), (2, -3), (-1, 0)

A: Consider the given points and the equation of the parabola. Obtain the system of equations with a, b…

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: The surface of a mountain is modeled by the equation h(x, y) = 7000 - 0.001x2 - 0.004y2. A mountain…

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

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Q: dy 20 yx %3D

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

A: Given :          The equation of directrix of the parabola is x + 1 = 0          The length of the…

Q: Find equations for two lines through the origin that are tangent to the ellipse x - 8x +y +5 = 0. YI…

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Q: Find the coordinates of the center of the curve whose equation is 16x2-25y2+160x- 200y+400=0. 4,5 O…

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Q: x? + y² = 2 (2,0) at the point b) Find an equation for the tangent to the ellipse 4

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

Q: Find the equation of one of the tangents to the ellipse 2x² + 4y² = 48 with slope of mt = 1.

A: The given equation of the ellipse is, 2x2+4y2=48 To find the slope of the tangent to the ellipse, we…

Q: Determine the relation of the ellipse x + 4y° = 32 and the line 2x +y-1 0.

A: To Determine: the relation between the ellipse x2+4y2=32 and the line 2x+y-1=0 Given: we have two…

Q: Find the length of the curve. x- 4t°, y= 6t, 0sts 3

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

A: Consider the given parabola y=x2+4 and the line y=2x+2. Use online graphing calculator and sketch…

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: Determine the relation of the ellipse x + 4y = 32 and the line 2x +y-1 0.

A: Step:-1 Given conic and line is x2 +4y2 =32   and 2x+y-1=0 To find the relation between the ellipse…

Q: 6. Y = %3D x2-4x+4

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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 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: Find equations of both the tangent lines to the ellipse  x2 + 7y2 = 63  that pass through the point…

A: consider (x0 ,y0) be an any point on ellipse

Q: The equation x2 − xy + y2 = 3 represents a “rotated ellipse”, that is an ellipse whose axes are not…

A: Given: The equation x2 − xy + y2 = 3 represents a “rotated ellipse”, that is an ellipse whose axes…

Q: Find the point on the parabola y=x^2 that is closest to the point (6,3) what is the distance between…

A: Given: To find the point on the parabola y=x2 that is closest to the point (6,3) what is the…

Q: Find the length of the diameter of the ellipse 3x2+y2 +2x-6y=0. Which has a slope of 2.

A: Ellipse

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

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Q: FInd the equations of the tangents with slope m=-2/9 to the ellipse 4x^2+9y^2=40

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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 the equation of the parabola with directrix x + 1 = 0, axis y = 2, and latus rectum 2.

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Q: Sketch the curve with equation x2/3 + y2/3 = 4 and use symmetry to find its length.

A: Arc Length formula in the interval [a,b] is given by, L=∫ab1+dydx2 dx This is applied only when dydx…

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 the equation of the parabola with directrix y = 3, axis x = 0, and latus rectum 4

A: Given: Equation of directrix:y=3……1Equation of axis:x=0……2Length of latus rectum:4……3

Q: Find the equation of the parabola with directrix x + 2 = 0, axis y = 4, and latus rectum 4.

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Q: Does the parabola y=2x^2-22x+3 have a tangent whose slope is -2? If so, find an equation for the…

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Q: 9. Find equations for two lines through the origin that are tangent to the ellipse 1² – 4x + 4y² =…

A: We have to find

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

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