find the equation of parabola whose directrix is 2 x minus 3 Y + 4 equal to zero and vertex at 5, - 4
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Step-by-step explanation:
axis of a parabola is perpendicular to the directrix equation of line is perpendicular to the given line
given line 2x-3y+4=0 -------------(1) ,slope = -2/-3 and perpendicular slope = -3/2 and given point is (5,-4) so equation of line is y +4 = -3/2 (x-5) ⇒2y+8=-3x+15
2y+3x=7-------------(2) solving first and second we get x=1 and y=2
now vertex is mid point of focus now using mid point formula
(x+1/2 , y+2/2 ) =(5,-4) equating we get x=9 and y= -10
now by defination of conic SP =ePM
now squaring both side we get
9x²+4y²+284y+218x+12xy+2337=0
use( a+b+c)²= a²+b²+c²+2ab+2bc+2ca
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