The distance of the focus of x²-y²=4 , form the directrix which is nearer to it, is

Step-by-step solution

Given equation of hyperbola is x ²- y ²=4 or x ² 4 - y ² 4 =1 ( a ²= b ²=4 ) Now, b ²= a ² ( e ²-1 ) aligned 4 &=4 ( e ²-1 ) e = 2 aligned Equation of directrix x = a e x = 2 2 x = 2 x - 2 =0 and the focus =( ae , 0)=( 2 2 , 0)=(2 2 , 0) The nearest distance of focus from directrix = | 2 2 - 2 1 |= 2