Question

The locus of the foot of the perpendicular drawn from the centre to any tangent to the ellipse x²/a² + y²/b² = 1 is –

• A. A circle
• B. An ellipse
• C. A hyperbola
• D. None of these

Answer 1

Answer: (D)

None of these

Answer 2

Equation of any tangent to the ellipse is

y = mx + $\sqrt{a^{2}m^{2} + b^{2}}$ … (1)

Equation of the line through the centre (0, 0) perpendicular to (1) is

y = (–1/m) x … (2)

Eliminating m from (1) and (2) we get the required locus of the foot of the perpendicular

as y = –$\frac{x^{2}}{y}$ + $\sqrt{a^{2}\frac{x^{2}}{y^{2}} + b^{2}}$

or (x² + y²)² = a²x² + b²y².

Which does not represent a circle, an ellipse or a hyperbola.