Find an equation of the ellipse and graph it Center at 1 2 F

Find an equation of the ellipse and graph it. Center at (1, 2); Focus at (1, 4); contains the point (2, 2)

centre ( 1,2)

focus ( 1,4)

point ( 2,2)

standrad equation of ellipse is

(y-k)^2/a^2 + ( x-h)^2/b^2 = 1

where , h , k = centre

distance between foci and centre = c = 2 units

hence , c^2 = a^2 - b^2

2^2 = a^2 - b^2

4 = a^2 - b^2 ---------------- equation 1

from standard equation

(y-k)^2/a^2 + ( x-h)^2/b^2 = 1

plugging the centre and a point in the equation

(2-2)^2/a^2 + (2-1)^2 / b^2 = 1

b^2=1

a^2 = 5 ( from equation 1)

hence, equation of ellipse is

(y-2)^2 / 5 + (x-1)^2/ 1 = 1