=1 ...(i) To find Equation of tangent and normal at point (
a
√2
,
b
√2
) We have to find
dy
dx
. Slope of tangent =
dy
dx
|(
a
√2
,
b
√2
)=mT Now, differentiating Eq. (i) w.r.t. x
2x
a2
+
2y
b2
dy
dx
=0
dy
dx
=−
2x
a2×
2y
b2
=−
b2
a2
(
x
y
) ∴ mT=−
b2
a2
(
a
√2
b
√2
)=−
b
a
and mN=−
1
mT
=
a
b
Equation of tangent (y−
b
√2
)=−
b
a
(x−
a
√2
) ...(ii) Equation of normal (y−
b
√2
)=
a
b(x−
a
√2
)
...(iii) To find Area of triangle made by tangent, normal and X-axis.We have to find points on X-axis cut by tangent and normal, i.e B and C For B Put y=0 in Eq. (ii) ⇒−
b
√2
=−
b
a
(x−
a
√2
)
a
√2
=x
−a
√2
(x=√2a) ∴ B is (√2a,0) For C Put y=0 in Eq. (iii) ⇒−