Question

Area of the triangle formed by the x-axis and tangent and normal drawn to the curve y = x² at (1, 1) is equal to

• A. 3 sq. units
• B. 5/4 sq. units
• C. 4 sq. units
• D. 2 sq. union

Answer 1

Answer: (B)

5/4 sq. units

Answer 2

y = x² ⇒ $\frac { d y } { d x }$ = 2x

Equation of tangent at P(1, 1) is;

(y – 1) = 2(x – 1) i.e. y = 2x – 1

Thus T ≡ $\left( \frac { 1 } { 2 } , 0 \right)$

Equation of normal PN at P(1, 1) is,

(y – 1) = $- \frac { 1 } { 2 }$(x – 1) i.e. 2y = −x + 3

Thus N ≡ (3, 0)

Required area = A_PP1T + A_PP1N

$= \frac { 1 } { 2 } \cdot 1 \cdot \frac { 1 } { 2 } + \frac { 1 } { 2 } \cdot 2 \cdot 1 = \frac { 5 } { 4 }$ sq. units.