AP EAMCET Engineering 18 Sep 2020 Shift 2 Paper

Given,
Focus S=(6,2)
Centre C=(1,2)=(h,k)
Point P=(4,6)
Required Equation of ellipse is
‌

(x−1)2

a2

+‌

(y−2)2

b2

=1....(i)
Since, Eq. (i) passes through P(4,6)
‌

(4−1)2

a2

+‌

(6−2)2

b2

=1
‌

9

a2

+‌

16

b2

=1.....(ii)
Since, Focus =(6,2)
(h+ae,k)=(6,2)
∴‌‌h+ae=6
k=2
1+ae=6
ae=5
a2e2=25
b2=a2(1−e2)
b2=a2−a2e2
b2=a2−25
a2=b2+25 ....(iii)
Put a2 value in Eq. (ii),
‌

9

b2+25

+‌

16

b2

=1
9b2+16(b2+25)=b2(b2+25)
9b2+16b2+400=b4+25b2
b4=400
b2=20
From Eq. (iii),
a2=20+25
a2=45
Put a2,b2 Value in Eq. (i),
‌

(x−1)2

45

+‌

(y−2)2

20

=1
[∴ Answer written in the paper was wrong in RHS it should be 1]