Math, asked by priyankyayde1974, 10 months ago

find the equation of parabola whose directrix is 2 x minus 3 Y + 4 equal to zero and vertex at 5, - 4​

Answers

Answered by chahararjun98
0

Answer:

I don't know your question

Answered by sumitgraveiens
3

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

\sqrt{(x-9)^{2} }+(\sqrt{} y+10)^{2} =\frac{2x-3y+4}{\sqrt{13} }   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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