IIT JEE , AIEEE Forum - Mathematics , Analytical Geometry - 2-5 POINTER REWARD

patiala_boy91

how to use shifting of origin in

PARABOLA

LIKE TO FIND IT'S EQUATION HAVING FOCUS (-6,-6)

VERTEX (-2,2)

SOLVE IT

wnnaiit

shift the origin to (-2,2)

x=X-2

y=Y+2

focus becomes (-4,-8)

length of latus rectum is (16*5^1/2)

but i dont think that shifting of origin will help

EFFORT

dont know how to use parameteric form

rhd92781

eqn of axis is 2x-y-18=0 (passing trgh (-2,2), (-6,-6))
directrix is prpndiclar to axis so slope =-1/2
vertex is mid point of focus & intersection of directrix & axis
so intersection point comes(2,10)
eqn of directrix comes x+2y-22=0
apply PF^2=PS^2
(x+6)^2 + (y+6)^2 = (x+2y-22)^2/5

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