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Find the equation of a parabola with focal point (-8,-2) and directrix y-2x+9=0.

Find the equation of a parabola with focal point (-8,-2) and directrix    y-2x+9=0.

Grade:11

1 Answers

Arun
25763 Points
2 years ago
PS =PM 
PS is distance of point from focus
PM is perpendicular distance of point from a line
√(x+8)^2 + ( y+2)^2 = | -2x+y +9 / √ 4+ 1 |
Squaring on both side 
X^2 +64 + 16x + y^2 + 4 y + 4 = (-2x+y+9)^2 / 5
 = 4x^2 +y^2 +81 - 4xy + 18y - 36 x /5
5x^2 + 5y^2 + 20y + 80 x + 340 = 4x^2 + y^2 -4xy +18y -36x + 81
 

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