Saved Bookmarks
| 1. |
Find the focus of the parabola whose vertex is at (- 1, 2) and the directrix x + 2y + 1 = 0 |
|
Answer» Let P(x,y) be any point on the parabola whose focus is S(−1,−2) and the DIRECTRIX x−2y+3=0.Draw PM perpendicular to directrix $$x - 2y + 3 = 0$$ Then by DEFINITION SP=PM⇒SP 2 =PM 2 ⇒(x+1) 2 +(y+2) 2 =( 1+4 x−2y+3 ) 2 ⇒5[(x+1) 2 +(y+2) 2 ]=(x−2y+3) 2 ⇒5(x 2 +y 2 +2x+4Y+5)=(x 2 +4y 2 +9−4xy+6x−12y)⇒4x 2 +y 2 +4xy+4x+32y+16=0 This is the equation of the required parabola |
|