Work out the value of 'c' to find the coordinates of two focus We have [tex]a^2=8^2[/tex] and [tex]b^2=7^2[/tex] [tex]c^2=a^2+b^2=8^2+7^2=64+49=113[/tex] [tex]c= \sqrt{113} [/tex]
The coordinate of foci is [tex](2- \sqrt{113}, 1) [/tex] and [tex](2+ \sqrt{113}, 1) [/tex]
Notice that the y-coordinate of the focus is the same with the y-coordinate of the centre, so we'll only need to work out the horizontal distance between one foci to the centre (the centre of a hyperbola is the same distance to both focus)
Distance from foci to centre = [tex](2+ \sqrt{113})-2=12.6-2=10.6[/tex] --------------------------------------------------------------------------------------------------------------
Option B
Centre (-2, 3) c² = a² + b² = 19² + 11² = 482 c = √482 c = 21.95
The coordinates of focus = (-2+21.95, 3) and (-2-21.95, 3) = (19.95, 3) and (-23.95, 3)
Distance from one foci to the centre is = 19.95 - (-2) = 21.95 units If the other foci is used for the calculation, the answer will be the same ---------------------------------------------------------------------------------------------------------------
Option C
Centre (1, 2) c² = 6² + 9² = 36 + 81 = 117 c = √117 c = 10.8
Coordinates of focus = ((1-10.8), 2) and ((1+10.8), 2) = (-9.8, 2) and (11.8, 2)
Distance between foci and centre = 11.8 - 1 = 10.8 units ----------------------------------------------------------------------------------------------------------
Option D
Centre (5, -3)
c² = 5² + 19² = 386 c = √386 c = 19.6
Coordinates of focus are ((5-19.6), -3) and ((5+19.6), -3) = (-14.6, -3) and (24.6, -3)