COMEDK Exam 2014 Solved Paper

Let equation of ellipse be

x2

a2

+

y2

b2

=1
Since it passes through the points (−3,1) and (2,−2)
∴

(−3)2

a2

+

(1)2

b2

=1‌and

(2)2

a2

+

(−2)2

b2

=1
⇒

9

a2

+

1

b2

=1 ....(i)
⇒

4

a2

+

4

b2

=1 .......(ii)
Multiply by 4 in Eq. (i) and subtracting Eq.(i) from Eq.(ii),
3a2=32⇒a2=

32

3

Subtracting in Eq. (i), gives

9×3

32

+

1

b2

=1
⇒

1

b2

=1−

27

32

=

5

32

⇒b2=

32

5

∴ Required equation is

3x2

32

+

5y2

32

=1‌or‌3‌x2+5y2=32