In the derivation, the difference between the distances from any point P on a branch of the hyperbola to foci of the hyperbola is set equal to the constant value of .
2a is used in the equation because the is a point on the hyperbola and it is the difference in the distances from this point to the foci.
This can be shown algebraically if we let a be the distance from the to the vertex. Then, the difference of the distances is (c + a) – .

Leslie started last week with $1200 in her checking account. during the week, she wrote the checks below. trans typ./ check no. date description of transaction payment/ debit deposit/ credit (+) balance 1,200 00 324 10/6 miller's food market 45.87 45 87 groceries 1,154 13 325 10/7 cyber center computer outlet 218.59 218 59 monitor 935 54 326 10/9 sandy's beauty salon 30.00 30 00 haircut and styling 900 59 deposit 10/10 paycheck 621.33 621 33 1,621 92 evaluate leslie's check register. a. leslie did a good job. everything is correct. b. the final balance is wrong; she did not add everything correctly. c. leslie should have written debit instead of deposit for the transaction type. d. leslie switched the debit and credit columns.