Question

If chords of contact of tangents from two points (x₁, y₁)

(x₂, y₂) to the ellipse $\frac{x^{2}}{52} + \frac{y^{2}}{13} = 1$ are at right angle then ratio of the product of abscissa’s and ordinates is

• A. –16:1
• B. 4:1
• C. 16:1
• D. None of these

Answer 1

Answer: (A)

–16:1

Answer 2

Equation of chord of contact of tangent from (x₁, y₁) to the ellipse $\frac{x^{2}}{52} + \frac{y^{2}}{13} = 1$ is $\frac{xx_{1}}{52} + \frac{yy_{1}}{13} = 0$

⇒ m₁ = slope = $\frac{- x_{1}}{4y_{1}}$

Again equation of chord of contact of tangent from

(x₂, y₂) $\frac{xx_{2}}{52} + \frac{x_{2}}{13} = 0$

m₂ = -$\frac{x_{2}}{4y_{2}}$

∴ m₁m₂ = -1

Now tangents are at right angle

⇒ $\frac{xx_{2}}{52} + \frac{x_{2}}{4y_{2}} = - 1$

⇒ $\frac{x_{1}x_{2}}{y_{1}y_{2}} = - \frac{16}{1}$