The equation x2- x   y + y 2  = 3  represents a “rotated ellipse,” that is, an ellipse whose axes are not parallel to the coordinate  axes. Find the points at which this ellipsecrosses the x -axis and show that the tangent lines at these points are parallel.

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 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: 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: The equation x2-xy+y2=1 describes an ellipse. Find the coordinates (x,y) of all the points on the…

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Q: Write the equation of the hyperbola centered at the origin, with length of the horizontal transverse…

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Q: Write the equation of the hyperbola centered at the origin, with length of the horizontal transverse…

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Q: Find the equation for the parabola that has its focus at the (−394,−4) and has directrix at x=−25/4

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Q: Find an equation of the ellipse having a major axis of length 12 and foci at (-1,-2) and (-9, -2).…

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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 the equation of the tangent to the hyperbola x2 - 4y2 = 9 at (5, 2).

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Q: 6. What is the equation for the slope of the ellipse+-1 at 1 at (x₁, ₁)? A. B. C. D. E. y' = -21 y'=…

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Q: What is the equation of the line tangent to the hyperbola = 1 at the point (V2a, b)? y = -a+b 26 V26…

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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: 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 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: 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: A parabola has an equation of y² = 4x. Find the nearest distance from the point (-3, 6) to the %3D…

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Q: The equation x 2 −xy +y 2 = 3 represents a rotated ellipse, that is, an ellipse wholes axes are not…

A: The given equation is: x2-xy+y2=3 Now the ellipse will cross the x-axis, when y become zero. Thus,…

Q: Suppose that point A(-4,0) lies on a parabola whose focus is at (5,3). What is the length of the…

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

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Q: Find the points on the ellipse x^2 + 9y^2 = 9 and the line x + y = 10 that are closest and farthest…

A: Distance between the two points: - The length of the line segment connecting two places is called…

Q: The equation x^2+ xy + y^2 = 1 forms an ellipse. In the second quadrant, the line tangent to the…

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Q: If it is projected to be out of the Philippine Area of Responsibility in a few days given an…

A: Standard form of a circle, x-h2+y-k2=r2 Where (h, k) is a center of a circle and r is a radius.

Q: Find the equation of the line tangent to the hyperbola x2 −y2 =16 at (5,3).   Give your answer in…

A: The line is tangent to the given hyperbola at (5,3).Tangent line is a straight line.Therefore, the…

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: 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: Write the equation of the hyperbola centered at the origin, with length of the horizontal transverse…

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

A: Ellipse

Q: What are the coordinates of the end points of the latus rectum of the parabola with equation a - 2z…

A: What are the coordinates of the end points of the latus rectum of the parabola with equation…

Q: Suppose a golf ball is driven so that it travels a distance of 200 feet as measured along the ground…

A: Given:A golf ball travels a distance of 200 feet as  measured along the ground and reaches an…

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 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 points of intersection of the parabola with equation 2x + y² + 4y – 2 = 0 and the line…

A: Here we find the intersecting point of parabola and the line.

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 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 orthogonal trajectory of family of parabolas represented by the equation…

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

Q: Find the equation of the parabola whose vertex lies at (0,-2) and directrix at x=2

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Q: Find the slope of the ellipse x^2 + 4y^2-10x- 16y +5=0 at the point where y=2+ 8 0.5 and x-7* O…

A: Given equation of the ellipse is as following: x2+4y2-10x-16y+5=0. We know that the slope of an…

Q: Suppose a golf ball is driven so that it travels a distance of 200 feet as measured along the ground…

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Q: Find the equation in standard form of a parabola whose focus is at (-3,-2) and whose directrix is x:…

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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: Given an ellipse x2/a2 +y2/b2= 1, a  b, find the  equation of the set of all points from which there…

A: (Note: We are entitled to solve only one question at a time) Given: x2a2+y2b2=1, where a≠b. To Find:…