If the sum of the slopes of the lines given by x2 - 2cxy - 7y2 = 0 is

1.	If the sum of the slopes of the lines given by x2 - 2cxy - 7y2 = 0 is four time their products, then the value of c is1. 12. -13. -24. 2
Answer» Correct Answer - Option 4 : 2 Concept: Let m1 and m2 be the slope of the line ax2 + 2hxy + by2 = 0 ⇒ m1 + m2 = \(\rm \dfrac {-2h}{b}\) ⇒ m1 . m2 = \(\rm \dfrac {a}{b}\) Calculations: Given equation is x2 - 2cxy - 7y2 = 0 Comparing with the equation ax2 + 2hxy + by2 = 0 ⇒ a = 1, h = - c, and b = - 7 Let m₁and m2 be the slope of the line x2 - 2cxy - 7y2 = 0 ⇒ m1 + m2 = \(\rm \dfrac {-2h}{b}= \dfrac{2c}{-7}\) ⇒ m1 . m2 = \(\rm \dfrac {a}{b}= \dfrac{1}{-7}\) Given, the sum of the slopes of the lines given by x2 - 2cxy - 7y2 = 0 is four time their products. ⇒ m1 + m2 = 4m1 m2 ⇒\(\rm \dfrac{2c}{-7} = \dfrac {4}{-7}\) ⇒ c = 2 Hence, if the sum of the slopes of the lines given by x2 - 2cxy - 7y2 = 0 is four-time their products, then the value of c is 2

If the sum of the slopes of the lines given by x2 - 2cxy - 7y2 = 0 is four time their products, then the value of c is1. 12. -13. -24. 2

Answer» Correct Answer - Option 4 : 2

Concept:

Let m1 and m2 be the slope of the line ax2 + 2hxy + by2 = 0

⇒ m1 + m2 = \(\rm \dfrac {-2h}{b}\)

⇒ m1 . m2 = \(\rm \dfrac {a}{b}\)

Calculations:

Given equation is x2 - 2cxy - 7y2 = 0

Comparing with the equation ax2 + 2hxy + by2 = 0

⇒ a = 1, h = - c, and b = - 7

Let m₁and m2 be the slope of the line x2 - 2cxy - 7y2 = 0

⇒ m1 + m2 = \(\rm \dfrac {-2h}{b}= \dfrac{2c}{-7}\)

⇒ m1 . m2 = \(\rm \dfrac {a}{b}= \dfrac{1}{-7}\)

Given, the sum of the slopes of the lines given by x2 - 2cxy - 7y2 = 0 is four time their products.

⇒ m1 + m2 = 4m1 m2

⇒\(\rm \dfrac{2c}{-7} = \dfrac {4}{-7}\)

⇒ c = 2

Hence, if the sum of the slopes of the lines given by x2 - 2cxy - 7y2 = 0 is four-time their products, then the value of c is 2