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

Q: Find an equation of the ellipse having a major axis of length 12 and foci at (5, 3) and (-3, 3). A…

A:

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: Situation 6. Find the slope of the ellipse x2 + 4y2 – 10x – 16y + 5 = 0 at the point where y = 2 +…

A: Shown below

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

A:

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

A:

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

A:

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

A:

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

A:

Q: Find the least and greatest distances from the origin to a point on the ellipse x²+4y²=16.

A: Topic:- geometry

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'=…

A:

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

A:

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

A:

Q: Find an equation of the ellipse having a major axis of length 10 and foci at (5,-1) and (-1, -1).…

A:

Q: Find the standard equation of the ellipse whose major and minor axes are the transverse and…

A: We need to find standard equation of ellipse.

Q: Find the equations of the osculating circles of the parabola y = 3(x – 2)2 at the points (2,0)

A:

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…

A:

Q: The equation x2- x   y + y 2  = 3  represents a “rotated ellipse,” that is, an ellipse whose axes…

A:

Q: 1. What is the equation of the line to the parabola y = x2 + 5x +1 through the 15 point at

A: Given, Parabola  y=x2+5x+1 Point 12, 154

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…

A:

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

A:

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

A:

Q: 64. Find equations of both the tangent lines to the ellipse x² + 4y2 = 36 that pass through the…

A: Given: The Equation of the ellipse is x2 + 4y2 = 36

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.

A:

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

A:

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

A:

Q: Write an equation for the ellipse. minor axis from (- 8, – 2) to (2, – 2); major axis from (- 3, -…

A:

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.

A:

Q: Find an equation for the ellipse of eccentricity 2 /3 that has the line x = 2 as a directrix and the…

A: To determine the equation of the ellipse.

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

A:

Q: 4x^2 + y^2 = 4 that are the farthest away from point (1,0)

A:

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 equation of a parabola that has focus at (-4,0) and directrix 2

A:

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 y = ax^2 + bx +c that passes through the points (-1,-4) (1,4), and…

A: topic  -  parabola

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: Find an equation of the ellipse having a major axis of length 10 and foci at (5, -1) and (-1, -1).…

A:

Q: Which is the equation of an ellipse with direcrices at x = =-4 and foci at (2,0) and (-2,0)

A: Center is the midpoint of the foci  midpoint of (2,0) and (-2,0) is : Directrix = -4

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

A:

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

A: