Question

find the equation of the parabola whose focus is (-1,1) and whose vertex is (1,2) also find it's axis and latus rectum​

Answer 1

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.

⇒2a+1=2;2b−1=1

⇒a=3,b=3

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

PS=PM

PS2=PM2

⇒(x−1)2+(y+1)2=5(x+2y−9)2

⇒4x2+y2−4xy+8x+46y−71=0

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

=2(42+22)

=2(25)=45

Answer 2

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.

⇒2a+1=2;2b−1=1

⇒a=3,b=3

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

PS=PM

PS2=PM2

⇒(x−1)2+(y+1)2=5(x+2y−9)2

⇒4x2+y2−4xy+8x+46y−71=0

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

=2(42+22)

=2(25)=45