Question

the equation of parabola with focus (-1,-2) and the directrix x-2y+3=0​

Answer 1

Answer:

focus{S} ≡ (-1,-2)

directrix ------->   x-2y+3=0

CONSIDER AN POINT ON PARABOLA  , THAT IS  POINT P WITH CO-ORDINATES   (h,k) .

IF POINT P IS ON PARABOLA THEN IT'S DISTANCE FROM FOCUS WILL BE EQUAL TO IT'S DISTANCE FROM DIRECTRIX.

THEREFORE,

[h-(-1)]^2  +  [k-(-2)]^2   =  [h-2k+3]^2 /5

5[h^2 + 1 + 2h + k^2 + 4 + 4k] =h^2 +6h -4k + 9 + 4k^2 - 12k

4h^2 + k^2 + 4h  + 36k +16 =0

NOW REPLACING [h,k] WITH [x,y] WE GET,

4x^2 + y^2 + 4x + 36y + 16 =0

THIS IS THE EQUATION OF PARABOLA.

HOPE IT HELPS...

MARK AS AN BRAINLIEST..