One of the hardest SAT algebra questions

What is the radius of the circle in the xy-plane determined by the equation 2x^2 - 6x + 2y^2 + 2y = 45. Good practice test question. #math #maths #mathematics #shorts

My initial upload had a small mistake! Thanks to @luismigueluribe914 for the comment. I have uploaded a corrected

References

Send me suggestions by email (address at end of many videos). I may not reply but I do consider all ideas!

If you purchase through these links, I may be compensated for purchases made on Amazon. As an Amazon Associate I earn from qualifying purchases. This does not affect the price you pay.

Book ratings are from January 2022.

My Books (worldwide links)

My Books (US links)
Mind Your Decisions: Five Book Compilation
A collection of 5 books:
"The Joy of Game Theory" rated 4.2/5 stars on 224 reviews
"The Irrationality Illusion: How To Make Smart Decisions And Overcome Bias" rated 4/5 stars on 24 reviews
"40 Paradoxes in Logic, Probability, and Game Theory" rated 4.1/5 stars on 38 reviews
"The Best Mental Math Tricks" rated 4.2/5 stars on 76 reviews
"Multiply Numbers By Drawing Lines" rated 4.3/5 stars on 30 reviews

Mind Your Puzzles: Collection Of Volumes 1 To 3
A collection of 3 books:
"Math Puzzles Volume 1" rated 4.4/5 stars on 87 reviews
"Math Puzzles Volume 2" rated 4.1/5 stars on 24 reviews
"Math Puzzles Volume 3" rated 4.2/5 stars on 22 reviews

2017 Shorty Awards Nominee. Mind Your Decisions was nominated in the STEM category (Science, Technology, Engineering, and Math) along with eventual winner Bill Nye; finalists Adam Savage, Dr. Sandra Lee, Simone Giertz, Tim Peake, Unbox Therapy; and other nominees Elon Musk, Gizmoslip, Hope Jahren, Life Noggin, and Nerdwriter.

My Blog

Twitter

Instagram

Merch

Patreon

Press

[MindYourDecisions]

My initial upload had a small mistake! Thanks to @luismigueluribe914 for the kind comment notifying me of the mistake!

[animezoneamv]

Just 2 months back I completed the whole circles JEE portions for 11th and you instantly make a video on it. Nice

[lucachu]

Omg I was out sick from school and in Geometry we were learning about the graphing a circle then you post this video!

[jameskelvin]

Another method:
The eqn of a circle is also given by
x²+y²+2gx+2hy+c=0
where centre is (-g, -h)
And radius is sqrt(g²+h²-c)
Given eqn in the qn can be arranged in
2x²+2y²-6x+2y-45=0
or, x²+y²-3x+y-(45/2)=0
or,
Here, g=-3/2, h=1/2, c=-45/2

={9/4+1/4+45/2}½
={5/2+45/2)½
=25½
=5.

[tonyromano]

Sir it’s 4am where i live, i just wanted a relaxing video to sleep… 😐

[j.r.]

This is the closest I've come to matching the sub-1-minute solutions given in these videos. :) I did it in about 2. Thanks for making the right-hand side work out to a nice perfect square.

[willowoodz]

1. divide by the common coefficient between the x and y variables.
2. "complete the square" by squaring the numbers that do not have an exponent (this is only for the numbers that are on the left side of the equation)
3. add those squared numbers (that should be in fractional form) onto both sides of the equation. disregard the left side now and focus on the right side with the answer.
4.make the fractional sum into a whole number.

[stealthemoon]

I had a question like this on the first SAT I took, and I absolutely loved it

[agastyavalisetty]

or u can use the general formulae from the conic section general formula theres a relation of coefficients directly for radius of circle or distance between focci of ellipse in conic section general formula but this works too

[maxhagenauer]

You can also solve for the 2 x values in the equation and then subtract them and divide by 2.

[d.m.b.]

I mean, from the level of olympiad problems to an easy peasy 11th standard problem.

[wwfewgrwegre]

another way: x^2+y^2+2gx+2fy+c=0
and use the formula r^2=g^2+f^2-c to get radius

[shy___art]

I just woke up and I'm watching this😂

[garvkumar]

jee aspirants be like: look what they need to mimic a fraction of our power

[rashjaks]

(x-h)^2+(y-k^^2=r^2 here r is radius and h and k are centre co ordinates . And to solve this q use completing the question formula and it’s very easy mentally solvable question . Being a jee aspirant ‘ye toh tatti’ type q hai

[hoangnhan]

I just took an exam and there is a question likes that. Sadly, I didn't watch this video =((

[tortoiseahoy]

Or else use the general equation of circle!

[acestar]

bro don't think i am mocking you, but seriously was this one of the hardest in SATs ?

[SameAsAnyOtherStranger]

This is another math "problem" that makes it easier to remember the formula because the solution fits handily into a reconscribed result. BTW- "reconscribed" is being used as a word in the wild on the internet.

[manishjaishi]

Piece of cake for OPT MATHS students, isn't it?