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  • The focus of parabola whose vertex is    whose equation of directrix is  <img alt="\mathrm {x+y+1

The focus of parabola whose vertex is  (4,5)  whose equation of directrix is  \mathrm {x+y+1=0,}  is
 

Option: 1

(-9,10)


Option: 2

(10,9)


Option: 3

(9,10)


Option: 4

None of these


Answers (1)

best_answer

Equation of directrix is  \mathrm {x+y+1=0} 
Directrix & axis of parabola are at right angles. Equation of axis  \mathrm {x-y+k=0} , passes through the vertex.

\mathrm {\therefore \quad k=1 \text { (Using }(4,5) \text { in } x-y+k=0)}

Required equation of axis is  \mathrm { x-y+1=0 }

Now vertex is mid point of NS.

\mathrm { \therefore \frac{x-1}{2}=4 \Rightarrow x=9 \text { and } \frac{y}{2}=5 \Rightarrow y=10 }

\therefore Focus is (9,10).

 

Posted by

rishi.raj

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