I want to know how to find the

Answered question

2022-03-19

I want to know how to find the vertices of the conic equation 

20x^2 +4y^2-800=0

Answer & Explanation

RizerMix

RizerMix

Expert2022-05-03Added 656 answers

20x2+4y2-800=0

Find the standard form of the ellipse.

Add 800 to both sides of the equation.

20x2+4y2=800

Divide each term by 800 to make the right side equal to one.

20x2800+4y2800=800800

Simplify each term in the equation in order to set the right side equal to 1. The standard form of an ellipse or hyperbola requires the right side of the equation be 1.

x240+y2200=1

This is the form of an ellipse. Use this form to determine the values used to find the center along with the major and minor axis of the ellipse.

(x-h)2b2+(y-k)2a2=1

Match the values in this ellipse to those of the standard form. The variable a represents the radius of the major axis of the ellipse, b represents the radius of the minor axis of the ellipse, h represents the x-offset from the origin, and k represents the y-offset from the origin.

a=102

b=210

k=0

h=0

Find the vertices.

The first vertex of an ellipse can be found by adding a to k.

(h,k+a)

Substitute the known values of ha, and k into the formula.

(0,0+102)

Simplify.

(0,102)

The second vertex of an ellipse can be found by subtracting a from k.

(h,k-a)

Substitute the known values of ha, and k into the formula.

(0,0-(102))

Simplify.

(0,-102)

Ellipses have two vertices.

Vertex1(0,102)

Vertex2(0,-102)

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