Question

Tangents are drawn from the points on the line x – y – 5 = 0 to x² + 4y² = 4, then all the chords of contact pass through a

fixed point, whose co-ordinates are –

• A. $\left( \frac{1}{5},\frac{4}{5} \right)$
• B. $\left( \frac{4}{5},\frac{- 1}{5} \right)$
• C. $\left( \frac{2}{5},\frac{2}{5} \right)$
• D. (5, 0)

Answer 1

Answer: (B)

$\left( \frac{4}{5},\frac{- 1}{5} \right)$

Answer 2

x – y – 5 = 0 … (1)

$\frac{x^{2}}{4} + \frac{y^{2}}{1}$ = 1 … (2)

Q any point on (1) is (h, h – 5)

\ equation of chord of contact is :

Ž xh + 4hy – 20y = 4

Ž h(x + 4y) – 4(5y + 1) = 0 …(3)

Q (3) always passes through point of intersection of

5y + 1= 0 and x + 4y = 0

Ž required fixed point (4/5, –1/5)