Question

find the parabola whose focus is 1,-1 and vertex is 2,1​

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

Answer verified by Toppr

1287 Views

Was this answer helpful