AP EAPCET 23-Aug-2021 Shift 2 Paper

Given, curves are : x2+y2=4x ...(i)
and x2+y2=8 ...(ii)
∵

dy

dx

is the slope of tangent drawn to curve.
Slope of the tangent drawn to curve (i) is
m1=

dy

dx

[ from curve (i)]
On differentiating Eq. (i) w.r.t. x

d

dx

(x2+y2)=

d

dx

(4x)
⇒2x+2y

dy

dx

=4
⇒

dy

dx

=

4−2x

2y

∴m1|(2,2)=

4−2×2

2×2

=0
On differentiating Eq. (ii) w.r.t. x,

d

dx

(x2+y2)=

d

dx

(8)
⇒2x+2y

dy

dx

=0
⇒

dy

dx

=

−2x

2y

=

−x

y

∴m2|(2,2)=

−2

2

=−1
tan‌θ=|

m2−m1

1+m1.m2

|=|

−1−0

1+0

|=1
⇒θ=tan−1(1)=

π

4

∵θ=sin−1(a) [Given]
⇒sin−1(a)=

π

4

⇒a=sin‌

π

4

⇒a=

1

√2