Question

OAB is a triangle where 'O' isthe origin. Equation of side ABis 3x + 4y - 19 = 0 and the excentreopposite to origin is (5,6). Thenthe equation to the pair oflines OA, OB is​

Answer 1

Given:

OAB is a triangle

Equation of side AB= 3x + 4y - 19 = 0

Excentre opposite to origin = (5,6)

To find:

The equation to the pair of lines OA, OB

Solution:

Since, 3x + 4y - 19 = 0

⇒ y = -3x/4 + 19/4

The above equation is in the form y = mx + c

On comparing, m = slope = -3/4

We know that the equation of a line in point-slope form is given by:

y - y1 = m (x - x1)

ATQ, y1 = 6 and x1 = 5

Substituting,

y - 6 = -3/4 (x - 5)

⇒3x² - 16 y² + 2xy - 10 = 0

Hence the equation is 3x² - 16 y² + 2xy - 10 = 0.