Question

locus of mid point of the portion between the axis of x cosa + y sin a = p where P is a constant is

• A. x² + y² = $\frac{4}{p^{2}}$
• B. x² + y² = 4p²
• C. $\frac{1}{x^{2}} + \frac{1}{y^{2}} = \frac{2}{p^{2}}$
• D. $\frac{1}{x^{2}} + \frac{1}{y^{2}} = \frac{4}{p^{2}}$

Answer 1

Answer: (D)

$\frac{1}{x^{2}} + \frac{1}{y^{2}} = \frac{4}{p^{2}}$

Answer 2

h = $\frac{\frac{P}{\cos\alpha} + 0}{2}$ ̃ cos a = $\frac{P}{2h}$

k = $\frac{0 + \frac{P}{\sin\alpha}}{2}$ ̃ sin a = $\frac{P}{2k}$

cos²a + sin² a = 1̃ $\frac{P^{2}}{4h^{2}} + \frac{P^{2}}{4k^{2}} = 1$

locus of (h, k) $\frac{P^{2}}{4x^{2}} + \frac{P^{2}}{4y^{2}} = 1$