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please explain too.
take any point on the parabola (x0,y0) then the distance between this point and the focus is given by sqrt[(x0 - 2)^2 + (y0 - 0)^2 and distance of the point from the directrix = 12
- sorry that distance from directrix is |y0 - 12|
so as the distance from the focus = distance from the directrix ( definition of a parabola) we have sqrt[(x0 - 2)^2 + (y0 - 0)^2 = (0 -12) simplify this to get the required equation
sorry - another typo its sqrt[(x - 2)^2 + (y - 0)^2] = (y -12)
- I change x0 and y0 to x and y
squaring both sides (x - 2)^2 + y^2 = (y - 12)^2 x^2 - 4x + 3 + y^2 = y^2 - 24y + 144 can you continue from here?
Could you go all the way please?
gave you best response
x^2 - 4x + 4 + y^2 = y^2 - 24y + 144 x^2 - 4x - 140 = -24y y = (-1/24)x^2 + (1/6)x - 35/6 = 0
I'm making a lot of typos today so I cant guarantee the answer but the method is right!
yeah its an answer could you help me with one more
no sorry gtg right now
I'm still not happy with that result
AH! the distance for directrix is |x - (-12)| = |x + 12| so we have (x - 2)^2 + y^2 = y^2 + 24x + 144 x^2 - 4x + 4 + y^2 = y^2 + 24y + 144 x^2 - 4x - 144 + 4 = 24x y = (1/24)x^2 - (1/6)x - 144/24 = 0 y = (1/24)x^2 - (1/6)x - 35/6 = 0 is the correct answer
the only problem with that is its not one of the options but I'm sure its correct
I'll check with wolfram alpha
http://www.wolframalpha.com/input/?i=equation+of+a+parabola+with+focus+%282%2C0%29+and+directrix+y+%3D+-12 there you go its correct
so there must be a typo in one of the choices looks like its C - which has 2 plus instead 2 negatives