Tangente común entre un círculo y una hipérbola (5 de 5)

all right where we left off we really were in the homestretch now we just have this messy arithmetic that we have to solve essentially find our slope and then we'll be able to figure out the y-intercept since we're actually gonna have to take the square root this hopefully will simplify into something let's just look at the let's just factor x 100 for square let's just worry about the radical 5 goes into 500 five goes into 500 a hundred times 99 is 95 for 95 can in fact it is 5 and so we can factor out this expression is a common factors like we're actually going to happen 1576 of this crazy thing and so let's see if we can factor this good practice your honor maybe there's a faster way to 12 times 12 times twelve times four we've gotten so far I don't want to make mistakes so 4 goes into 12 14 for 14 3 times 3 well to 24 33 thousand 136 once again this looks like is divisible by 4 again this is 4 times I should have just guested this whole thing for doesn't do goes into 31 7 times 28 84 this looks like it is divisible by 4 connealy simpler now 4 goes into 784 7 6 times and really if you are going to take the jei I do recommend being able to do this mental arithmetic much faster I'm clearly not capable of doing it faster so you have 196 and 196 this is divisible by 196 it goes my brain is fried 36 all right so we're taking the square root we could just take the square of each squared of this we could just take the square root of each of its term right over here simplify to this whole process whole video has been just 4 times 7 times 2 is 14 plus 5 let's see all of this stuff over here remember we want a positive slope so we want to add the 896 we're getting M Squared is equal to 104 plus 800 or negative plus 896 if we 104 from business over here we're gonna get we're gonna get 792 over 90 this is what ab squared that's equal to bi big arithmetic video hopefully we'll get the right answer let's hope that isn't the case justified by nine you get divided by nine these are both divisible by 11 over ten over ten five unbelievable it all simplified down to four fifths that's the slope of our line and now we just have to go back to one of these equations whichever one is simpler and find the y-intercept two over the square root of nine times oarfish - let me just I made a careless mistake hopefully I have it this is going to be equal to 9 times minus 20 over 5 so this is equal to the square root of 16 over 5 I'm running out of space so this is equal to so b is equal to z square 36 minus 20 is 16 so square root of 16 over square root of 5 for the square root 5 and we are done we now know the slope of that tangent line the thing that had a positive slope this equation is going to be y is equal to and if we simplify it because I remember problem that problems of practice from both sides and we get negative 2x plus square root of 5y minus 4 is equal to 0 it looks like they do if we just multiply everything times negative Y we multiply everything 2x minus the square root of 5y and we are done this was probably the most painful problem I've done in my life 2x minus the square root of 5y plus 4 the answer