Question

find the equation of the parabola with vertex (2,1)and focus (1,-1)
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Answer 1

Answer:

Focus is at S(1,-1)

Vertex is A(2,1)

Let the directrix be MZ and let coordinates of Z be (a,b)

Let the axis of parabola intersects directrix of parabola at Z.

Since, vertex is in between focus and directrix.

⇒

2

a+1

=2;

2

b−1

=1

⇒a=3,b=3

Let P(x,y) be any point on the parabola such that

PS=PM

PS

2

=PM

2

⇒(x−1)

2

+(y+1)

2

=

5

(x+2y−9)

2

⇒4x

2

+y

2

−4xy+8x+46y−71=0

Length of latus rectum =2(Distance between focus and directrix)

=2(

4

2

+2

2

)

=2(2

5

)=4

5

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Answer 2

Answer:

above answer is correct it will helpful for u