JEE Main · 2004 · 24 Apr 2004 · Offline · Straight Lines

If the sum of the slopes of the lines given by

x^{2} - 2 c x y - 7 y^{2} = 0

is four times their product, then c has the value

(A)1
(B)-1
(C)2✓ Correct
(D)-2

Answer: (C)

Solution

The equation

x^{2} - 2 c x y - 7 y^{2} = 0

is a pair of lines through the origin. Writing each as

y = m x

, substituting, and dividing by

x^{2}

gives

- 7 m^{2} - 2 c m + 1 = 0

, i.e.

7 m^{2} + 2 c m - 1 = 0

, whose roots are the two slopes. Hence

m_{1} + m_{2} = - \frac{2 c}{7}

and

m_{1} m_{2} = - \frac{1}{7}

. The requirement that the sum of slopes is four times their product gives

- \frac{2 c}{7} = 4 (- \frac{1}{7})

, so

- 2 c = - 4

and

c = 2

JEE Main · 2004 · 24 Apr 2004 · Offline · Single correct option

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