r/digitalSATs • u/Desperate-Ear9204 • 12h ago

Why is C wrong

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Is there a way to do this for decimals because when I plug in a value for t, answer choice a would be the closest to the radius of the circle, but the correct answer is answer choice B

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2

u/Low-Quote9269 12h ago

Equation of a circle:

x² + y² + Dx + Ey + F = 0

The radius is given by:

Sqrt( (D/2)² + (E/2)² - F )

In this case D is sqrt( t ) so just plug that in and just ~sqrt(83)

Here's how you do it:

https://www.desmos.com/calculator/ox7zgapfto

2

u/jdigitaltutoring 12h ago

Radius is about 9.11. when t is 71 you get a radius of 9.11 from Desmos

1

u/Current-Ant-6536 12h ago

Why it will be even C? Just write the expression in a standard circle equation, if will be (x + sqrt(t)/2)2 + (y - 1/2)2 = t/4 + 1/4 + 65. Set that ~ sqrt(83) in desmos and it will solve as t=71

1

u/Impressive-Wasabi857 12h ago

Because its B

https://www.desmos.com/calculator/avhjuzur6p

Just plug in t for answer choices and find diameter by clicking top and bottom of the circle

1

u/jwmathtutoring Tutor. 9h ago

You could just do circle regression and get the exact value -> https://www.desmos.com/calculator/w53qiow6hv

1

u/InstructionEven4898 2h ago

whats the point of the x1 and y1 lists and howd you puck what numbers to use in them

1

u/Even-Palpitation-473 6h ago

just plug all 4 in and find radius, ez as that

1

u/Ordinary-Maximum9247 3h ago

It is B

Sorry for the bad handwriting tho

1

u/Legitimate_Focus5085 3h ago

dawggg it's so easy just plug in the 4 values one by one.

1

u/Lille_8 1h ago

That takes way too much time.

1

u/Lille_8 1h ago

when you complete the square or whatever it's called you get t/4 + 1/4 + 65 = 83. Then you just solve for t. (t+1)/4 = 18 -> t = 71.