What is the standard form of the equation of the parabola with a directrix at x=5 and a focus at (11,-7)?

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Answer 1 · 2016-05-22T23:01:28

#(y+7)^2=12*(x-8)#

Your equation is of the form

#(y-k)^2=4*p*(x-h)#

The focus is #(h+p, k) #

The directrix is #(h-p) #

Given the focus at #(11,-7) -> h+p= 11 " and " k=-7#

The directrix # x=5 -> h-p = 5 #

#h+p= 11" " (eq. 1)"#
#h-p =5 " " (eq. 2)#

# ul("use (eq. 2) and solve for h")#

# " " h=5+p" (eq. 3)"#

# ul("Use (eq. 1) + (eq. 3) to find the value of " p)#

#(5+p)+p=11#

#5+2p=11#

#2p=6#

#p=3#

#ul("Use (eq.3) to find the value of " h ) #

#h=5+p#

#h=5+3#

#h=8#

# "Plugging the values of " h, p " and " k " in the equation "(y-k)^2=4*p*(x-h) " gives"#

#(y-(-7))^2=4*3*(x-8)#

#(y+7)^2=12*(x-8)#