Question

Find the equation of the parabola with focus (10, -3) and directrix y = 3.

Answer 1

→ Solution! - Definition !-( Parabola) -- A Parabola is a Jocus of point (ory such that its distance from a fixed point is equal to its distance from fixed fine. i's The fixed point is called focus of Parabola and fixed fine called Directrix of Parabola. In gwen problem focus = (10,-3) (10,-3) end directix Y-3 so so by definition we have Jp09) y = 3 M is (10,-3) S So we ſixo-10 + 15 +3} = 14-31 (y +3} = (4-3,² 2 2 4100-200 + y +9 toy = 8 + 9 by have PM = PS >> (21-10j3 + (473 > 32-200x-12 y +10 20 So equation of Parcebela 28-2008 1100-12y is Answer

a Concept used' A general equation of second degree ara+by+ Eh xy +2gx + afy tc= represent cli a ciocle if sto, a=b and h=o (10) a Parabola if sto and cab (lio a ellipse of oto and if cab liv a typerbola if oto and Bab h cand n² where a 20 l! h b at g f С 1 1a) 22 42 95 El 9 92-9548=995 =995 » 92² 954²_225=0 then a = 59 b=-25, hao, 99 p=0 C = -225 q low O -25 to O - 225 ab = ax.(-25) 2-985, h=o

& ob 80 So we have oto y cab y cob » x2 25 fo - represent a typerbola. (6) x+y+by -6 =0 a=o, b=1, C=-6, h=0, 9 = 2, f= 3 so Ret o 3 D) $(-) = ☆ to -6 3 h² = cab Þ=o, ab=0 So given equation represent a Parabola. of ty? cloo a = !, bal, heo, 9=9, fro C=-100 so you to = 0 o -100 Also hzo a=b=! debesent So given equestion a Circle