Question

Area enclosed by the curve y = f(x) that is being defined parametrically as x = y = is equal to

• A. π sq. units
• B. π/2sq. units
• C. $\frac { 3 \pi } { 4 }$ sq. units
• D. $\frac { 3 \pi } { 2 }$sq. units

Answer 1

Answer: (A)

π sq. units

Answer 2

Clearly ‘t’ can be any real number. Let t = tan θ ⇒ x = $\frac { 1 - \tan ^ { 2 } \theta } { 1 + \tan ^ { 2 } \theta }$

⇒ x = cos 2θ and y = $\frac { 2 \tan \theta } { 1 + \tan ^ { 2 } \theta }$ = sin 2θ

⇒ x² + y² = 1

Thus required area = π .1² = π sq. units.