Mathematics, 05.01.2021 16:00 jay8849

URGENT! Write the equation of the ellipse graphed below.

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URGENT!

Write the equation of the ellipse graphed below.
I already asked this question but still

Answers: 2

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Answer from: mooreadrian4123532

$\displaystyle \frac{(x-7)^2}{4}+\frac{(y+2)^2}{36}=1$

Step-by-step explanation:

Equation of The Ellipse

Given the center (h,k) and the length of the major and minor axis, we can write the equation of the ellipse as follows:

$\displaystyle \frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1$

If the major axis is a, then the ellipse is horizontal, if the major axis is b, then the ellipse is vertical.

The ellipse shown in the figure is centered at (7,-2). The major axis is b and it can be found by measuring the distance from the center up or down to any vertex. We find b=6 and a=2.

Thus, the equation of the ellipse is:

$\displaystyle \frac{(x-7)^2}{2^2}+\frac{(y+2)^2}{6^2}=1$

Operating:

$\mathbf{\displaystyle \frac{(x-7)^2}{4}+\frac{(y+2)^2}{36}=1}$

Answer from: Quest

5. y=6; de=7; fg=8

6. x=4.2; jl=14.2; mn=13

step-by-step explanation:

when chords cross inside a circle, the product of the segment lengths is a constant.

5. dh×eh = fh×gh

y = gh = dh×eh/fh = 3×4/2 . . . divide by the coefficient of gh

y = 6

of course, the total chord length is the sum of the lengths of its segments.

de = dh +eh = 3+4 = 7

fg = fh +gh = 2+6 = 8

6. this problem works the same way as the previous one.

x = lk = mk×nk/jk = 6×7/10 = 4.2

jl = jk +lk = 10 +4.2 = 14.2

mn = mk +nk = 6 +7 = 13

comment on chords and secants

you can think of the points h (problem 5) and k (problem 6) as points where the chords meet. a chord is part of a secant line, a line that intersects the circle in two points. one can also consider these points (h or k) to be the points where the respective secant lines meet.

then, the product that is a constant is the product of the distance from the meeting point (h or k) to one circle intersection with the distance from that meeting point to the other circle intersection. for problem 5, the constant is the product hd×he = hf×hg.

it turns out that this rule regarding the products of lengths to points of intersection is also true when the secants intersect outside the circle.

that is, you only need to remember one rule to work both kinds of problems.

Find the value of the variable and the length of each chord for #5 and #6.

Answer from: Quest

the sum of the lengths of any two sides of a triangle is greater than the length of the third side. if you take the three sides of a triangle and add them in pairs, the sum is greater than (not equal to) the third side. if that is not true, then it is not possible to construct a triangle with the given side lengths.

step-by-step explanation:

Which are the possible side lengths of a triangle?

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URGENT! Write the equation of the ellipse graphed below.

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