Write the standard form of 25x2 - 4y2 - 150x - 16y = -109

Find the coordinates of the center.

Question

Write the standard form of 25x2 - 4y2 - 150x - 16y = -109

Find the coordinates of the center.

anonymous · Answer

We have to use here Completion Of Square Method..

anonymous · Answer

right..would you be able to please explain that?

anonymous · Answer

It will take time but yeah I do if you will co operate with proper..

anonymous · Answer

Tell me what you get if you divide the coefficient of x by 2??

anonymous · Answer

75

anonymous · Answer

Yes....
Do you know this formula:

$$a^2 - 2ab + b^2 = (a-b)^2$$

anonymous · Answer

i think so

anonymous · Answer

Ok..
So we are to reduce the terms in this formula so that we can use it...

Now, take 25 common from:

25x^2 - 150x

What you will get?

anonymous · Answer

x^2-75x

anonymous · Answer

You are 25 common..
How you got 75??

anonymous · Answer

sorry i mean x^2-6x

anonymous · Answer

yes now we have to solve for this;

now divide the coefficient of x by 2..

anonymous · Answer

-3x

anonymous · Answer

really??

anonymous · Answer

What is coefficient of x??

anonymous · Answer

is it ...
25(x-3)^2-4(y+2)^2=100
or ((x-3)^2)/4 -((y+2)^2)/25 =1

anonymous · Answer

Wait I am checking..
I am just making him to solve and not yet solved by myself...

anonymous · Answer

are coordinates of the centre is 3,-2

anonymous · Answer

yes!! thank you!!!

anonymous · Answer

mention not