AP EAPCET 24-Aug-2021 Shift 1 Paper

∴ Centre and major axis of an ellipse are (0,0) and X-axis respectively.
Let

x2

a2

+

y2

b2

=1 be the equation of ellipse.
According to question it will pass through (−3,1) and (2,−2)
⇒

9

a2

+

1

b2

=1 ...(i)
and

4

a2

+

4

b2

=1
⇒

1

a2

+

1

b2

=

1

4

...(ii)
Subtract Eq. (ii) from Eq. (i), we get

9

a2

−

1

a2

=1−

1

4

⇒

8

a2

=

3

4

⇒a2=

32

3

By Eq. (i), we get

9

32 3

+

1

h2

=1
⇒

27

32

+

1

b2

=1
⇒

1

b2

=1−

27

32

⇒

1

b2

=

32−27

32

⇒

1

b2

=

5

32

⇒b2=

32

5

∴ Equation of ellipse

x2

32 3

+

y2

32 5

=1
⇒

3x2

32

+

5y2

32

=1
⇒3x2+5y2=32