Question

The locus of the point of intersection of the tangents to the circle x = r cosq, y = rsinq at points whose parametric angles differ by /3, is-

• A. x² + y² = $4 ( 2 - \sqrt { 3 } ) r ^ { 2 }$
• B. 3(x² + y²) = 1
• C. x² + y² = $( 2 - \sqrt { 3 } ) r ^ { 2 }$
• D. 3(x² + y²) = 4r²

Answer 1

Answer: (D)

3(x² + y²) = 4r²

Answer 2

Point of intersection R (h, k) is given by

h = , k =

" q – a = $\frac { \pi } { 3 }$

̃ $\left( \cos \frac { \theta + \alpha } { 2 } \right) ^ { 2 } + \left( \sin \frac { \theta + \alpha } { 2 } \right) ^ { 2 } = 1$

$\left( \frac { \sqrt { 3 } } { 2 } \frac { \mathrm {~h} } { \mathrm { r } } \right) ^ { 2 } + \left( \frac { \sqrt { 3 } } { 2 } \frac { \mathrm { k } } { \mathrm { r } } \right) ^ { 2 } = 1$