AP EAMCET2013MathematicsPair of Lines
The equation of the pair of lines passing through the origin whose sum and product of slopes are respectively the arithmetic mean and geometric mean of 4 and 9 is
Options
- A12 x^2-13 x y+2 y^2=0
- B12 x^2+13 x y+2 y^2=0
- C12 x^2-15 x y+2 y^2=0
- D12 x^2+15 x y-2 y^2=0
Correct answer
A. 12 x^2-13 x y+2 y^2=0
Step-by-step solution
Let m₁ and m₂ be the slopes of lines. Then, m₁+m₂= arithmetic mean = 13 2 and m₁ m₂= geometric mean = 36 =6 . Now, equation of the pair of lines passing through the origin is (y-m₁ x ) (y-m₂ x )=0 y^2- (m₁+m₂ ) x y+m₁ m₂ x^2=0 Using Eq. (i) and (ii), we get aligned y^2- 13 2 x y+6 x^2 & =0 12 x^2-13 x y+2 y^2 & =0 aligned