Find the points on the ellipse 4.x² + y° = 4 that are farthest from (1, 0). Hint: Begir with the distance formula. (-t. 똥) and (-t. 속), The points are 3 The points are (0, 1) and (0, -1). (글, 폴) (글, 골), V3 V3 2 ' The points are 2 2 The points are (글, v3) and (글, -v3).

Q: What point on the parabola y=3−x2 is closest to the point ​(3​,3​)?

A: Basic differentiation is required.

Q: Find the standard equation of the hyperbola. Two corners of auxiliary rectangle at (−4 ,−7) and (0…

A: Given: The two corners of the auxiliary rectangle of a hyperbola are at -4,-7 and 0,0 and transverse…

Q: Finally, determine a. The parabola passes through the point (0, 5). Substitute the values of x and y…

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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: Let S be the quadric with equation 36x² – 4y² – 9z2 – 36x = 0 • Classify the graph of S…

A: Given, S is the quadric with the equation                                36x2-4y2-9z2-36x=0

Q: A soccer ball is kicked from a point 23 m to the left of the half way line and lands at a point 17 m…

A: We use the equation in the form y=a(x-r)(x-s) Given Data: r=-23 and s=17

Q: 8. Determine the Equation of the Hyperbola if the Transverse Axis is 8 and the Foci are at (0, ±6)

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Q: center, horizontally, is the car when it is at an altituue Ul 23 IL! 2. A truck has to pass under an…

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Q: Determine the equation of the parabola with the directrix z = 3 and focus (0, 7). O y = 8 (z – 5) O…

A:

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 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: Two tanks are participating in a battle simulation. Tank A is at point (325, 810, 561) and tank B is…

A:

Q: What is the equation of the directrix of the parabola having a vertex at (6,0), passing through…

A: Given:- What is the equation of the directrix of the parabola having a vertex at (6,0), passing…

Q: find the equation of the tangent line through the point (2,-2) to the hyperbola x2-y2=16.

A:

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

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 parabola with directrix y = 3, axis x = 0, and latus rectum 4. (two answers…

A: The standard equation of the parabola is (y-k)=4a(x-h)2, where h and k are the coordinates of the…

Q: what is the equation of a parabola with a vertex at (4, 8) and a directrix at y=5

A:

Q: What point on the parabola y=(6−x)2 is closest to the point (6​,6​)?

A:

Q: Find an equation of the ellipse with foci at (-4, 3) and (-4, –9) and whose major axis has length…

A:

Q: Find equations for the osculating circles of the parabola y=0.5x2 at the points (0,0) and (-1,1/2).

A:

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

A: Given equations are,

Q: Regarding the orbit of the planet Mercury, we know, according to the National Encyclopedia, that it…

A: Given information: The minimum distance to the sun is 0.31 AU and that the maximum distance is 0.47…

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 the points on the ellipse 3x2 + y2 = 3 that are farthest away from the point (1, 0). What I…

A:

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: 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: If tangent lines to the hyperbola 9x2 − y2 = 36 intersect the y-axis at the point (0, 6), find the…

A:

Q: You have a parabolic bowl in the shape of the equationz=x^2+y^2, from z= 0 to z= 10. If you left the…

A: Let the parabolic bowl is filled till some height, h in..  So, the volume of the water in the bowl…

Q: Find the point on the ellipse x2 + 3y + 2xy = 6 with the greatest x-coordinate. (Use decimal…

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

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

A: Consider the ellipse, x24+y2=2

Q: The parabola y=x^2y=x2y, equals, x, squared is shifted up by 777 units and to the left by 111 unit.…

A:

Q: Find the equation of the hyperbola with center at (-3,3); transverse axis parallel to y-axis; length…

A:

Q: What point on the parabola y = 3- x² is closest to the point (3,3)? The point on the parabola y = 3…

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

A:

Q: What point on the parabola y = 1-x is closest to the point (1,1)? The point on the parabola y = 1-x2…

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

A:

Q: 10. 25x2 - 9y2 = 144           11. x2 + y2 = 225           12. x2 + 3y2 = 3

A:

Q: Two large airship hangars were built in Orly, France, in the early 1900s but were destroyed in World…

A: (a). It is given that, the length of hangars is 175 m, the width of the hangers is 90 m and the…

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: 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 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: What is the equation of normal to the ellipse 9y^2 + 4x^2 = 25 at (2,-1) ?

A: Slope of normal is -dx/dy  So we differentiate both sides with respect to x Then we plug x=2 and…

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

A: Solution is here

Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.