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The focus and directrix of a parabola are (1,2) and x + 2y + 9 = 0 then equation of tangent at vertex is ?

The focus and directrix of a parabola are (1,2) and x + 2y + 9 = 0 then equation of tangent at vertex is ?

Grade:12

1 Answers

Vikas TU
14149 Points
6 years ago
Dear Student,
let eq of axis y=mx+c
perpendicular to x+2y+9=0 so m=2
         =>c=0 , so axis is y=2x
let K is intersection of directrix and axis. To find K solving eqn. of directrix and axis, we get K=(-9/5 , -18/5)
so vertex= (1-9/5)/2 , (2-18/5)/2 = (-4/10, -4/5)
slope of tangent= -1/2 (as perpendicular to axis)
y=-x/2 +c
=>(-4/10, -4/5)=-4/5=4/20+c =>c=-1
so, eqn of tangent is y=-x/2 -1 (Ans)
Cheers!!
Regards,
Vikas (B. Tech. 4th year
Thapar University)

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