TS EAMCET 7 May 2018 Shift 1 Solved Paper

If a line y=mx+c is tangent to the ellipse

x2

a2

+

y2

b2

=1
Then, c2=m2a2+b2
The line y=−4x−p is tangent to ellipse x2+3y2=3⇒

x2

3

+

y2

1

=1, then
p2=3×16+1
p2=49
p=7
Again, the line y=mx+c is normal to the ellipse

x2

a2

+

y2

b2

=1
Then, c2=

m2(a2−b2)2

a2+b2m

Therefore, line 16x+qy+14=0 is normal to ellipse

x2

33

+

y2

33 8

=1

196

q2

=

256 q [33− 33 8 ]2

33+ 33 8 × 256 q2

1

q2

=

33

q2+32

q2=1
q=1
Then,p+q=7+1=8