Question

O(0, 0), A(1, 2), B(3, 4) are the vertices of ΔOAB. The joint equation of the altitude and median drew from O is ______ 

विकल्प

• x² + 7xy - y² = 0 

• x² + 7xy + y² = 0 

• 3x² - xy - 2y² = 0 

• 3x² + xy - 2y² = 0

Answer 1

O(0, 0), A(1, 2), B(3, 4) are the vertices of ΔOAB. The joint equation of the altitude and median drew from O is 3x² + xy - 2y² = 0.

Explanation:

OD is the median

∴ D ≡ `((1 + 3)/2, (2 + 4)/2)`

⇒ D ≡ (2, 3)

Equation of OD is y = mx

⇒ y = `3/2x` ⇒ 3x - 2y = 0

Slope of line AB = `2/2 = 1`

Given, OE ⊥ AB

∴ Slope of OE= -1

Equation of OE is y = mx

⇒ y = -x ⇒ x + y = 0

∴ Joint equation of median and altitude is

(3x - 2y) (x + y) = 0

⇒ 3x² + xy - 2y² = 0