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

Q: ...***... .. . .. The area of an ellipse with axes of length 2a and 2b is nab. The percent change in…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: What is the length of the latus rectum (LR) of the parabola y = -÷(x – 2)“ + 5?

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Q: What is the nearest distance from the point P(6,0) to the parabola? y^2=8x

A: GivenP(6.0)y2=8x To find nearest distance

Q: What is the length of the major axis of the ellipse defined by the equation: x2 + 5(y – 2)2 = 5?

A: The given equation is x2+5y-22=5 To find the length of the major axis of the ellipse.

Q: Find a parabola with equation y = ax2 + bx + c that has slope 8 at x = 1, slope −12 at x = −1, and…

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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: What is the (unsigned) distance between the vertex and the focus of the parabola given by (x + 4)² =…

A: Given parabola equation,x + 42 = 19y + 5

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 a parabola with equation  y = ax2 + bx + c  that has slope  13  at x = 1, slope  −19  at x =…

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Q: Show that the center of the osculating circle for the parabola y = x2 at the point (a, a2) is…

A: We need to show that the centre of the osculating circle for the parabola y = x2 at the point (a,…

Q: The area of the triangle formed by the tangent and the normal to the parabola y = 4ax both drawn at…

A: Given  the parabola y² = 4ax both drawn at the same end of the latus rectum and the axis of the…

Q: What is the measure of the focal width of the parabola y+2y+4x-3=0 ?

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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: 6. What is the equation for the slope of the ellipse+= 1 at (x₁, yi)? A. B. C. D. E. y' = y' = b²y₁…

A: We have to find the equation of the slope of ellipse at the point (x1,y1).

Q: . What is the snortest distance between the parabola y=2x² and the line y=4x-4

A: Shortest distance between two curves are always along the common normal.

Q: Find the point on the ellipse 4x2ty3=4 that are farthest away from the point (1,0) 4x27y2-4

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Q: for the ellipse 4x^(2) +y^(2) +24x -2y +21 = 0, find its area

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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: 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: Find a point on the parabola y - x* + 9 which is closest to the origin.

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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: Find the minimum distance from the point (4,2) to the parabola y2 = 8x.

A: We have to find the minimum distance from the point (4,2) to the parabola y2=8x.

Q: .... .. ......... ....*.*. ..* * ..... The area of an ellipse with axes of length 2a and 2b is nab.…

A: As per our guidelines , we can only solve first question. Please resubmit other questions as next…

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 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: 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: 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: 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: What is the area of the ellipse x² 16 + y² 9 = 1?

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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: Find the point on the parabola y=x2 closest to (6,3

A:

Q: Find the points on the ellipse 3x² + y“ = 3 that are farthest away from the point (1, 0).

A: For the Given Ellipse 3X2+y2=3 ,Points that are  Farthest away from the point (1,0) is calculated as…

Q: By differentiating implicitly, find the slope of the hyperboloid 22 + y? – 22 = 1 in the x-direction…

A: We have to find slope of the hyperboloid x2+y2-z2=1 in the x-direction at the points (a) 1,2,2 (b)…

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: 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 shortest distance of the point (6,3) to the parabola y=x2

A:

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: 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: 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:…

Vertices Of An Ellipse

In the study of the conic section of the geometry, An ellipse is a plane curve surrounding two focal points, or foci where the set of all locus of points in the plane has their sum of the distances to the two foci is constant. On the ellipse curve, it is the intersection point of the main axis. In an ellipse graph, the center of the axis is the midpoint of the line segment connecting the foci. The major axis is the line section that runs through the ellipse's foci, while the minor axis runs through the middle and is perpendicular to the major axis.. The ellipse has two endpoints on the major axis which are known as the vertices (in plural), vertex in the singular. The equation of the major axis is 2a, the equation of the minor is 2b and the distance between the major axis and minor axis is 2c. The semi-major axis has a length of a and the semi-minor axis has a length of b. The ellipse's vertices are determined by the elliptical orbit's equation and graph.