Question

Locus of the foot of the perpendicular drawn from the centre upon any tangent to the ellipse $\frac{x^{2}}{a^{2}}$+ $\frac{y^{2}}{b^{2}}$= 1, is –

• A. (x² + y²)² = b² x² + a²y²
• B. (x² + y²)² = b²x² – a²y²
• C. (x² + y²)² = a²x² –b²y²
• D. (x² + y²)² = a²x² + b²y²

Answer 1

Answer: (D)

(x² + y²)² = a²x² + b²y²

Answer 2

Centre ŗ (0, 0)

any tangent y = mx + $\sqrt{a^{2}m^{2} + b^{2}}$

Ž mx – y + $\sqrt{a^{2}m^{2} + b^{2}}$ = 0

Let foot is (h, k) so mh – k + $\sqrt{a^{2}m^{2} + b^{2}}$ = 0

and m = – $\frac{h}{k}$

So locus – $\frac{h^{2}}{k}$– k + $\sqrt{a^{2}\frac{h^{2}}{k^{2}} + b^{2}}$= 0

Ž (h² + k²)² = a²h² + b²k²

or (x² + y²)² = a²x² + b²y²