Question

Let PQR be right-angled isosceles triangle right angled at P(2, 1). If the equation of the line QR is 2x + y – 3 = 0 then the combined equation of the pair of lines PQ and PR is

(a) 3x2 - 3y2 + 8xy + 20x + 10y + 25 = 0

(b) 3x2 - 3y2 + 8xy - 20x - 10y + 25 = 0

(c) 3x2 - 3y2 + 8xy + 10x + 15y + 20 = 0

(d) 3x2 - 3y2 - 8xy - 15y - 20 = 0

Answer 1

Correct option**(b) 3x2 - 3y2 + 8xy - 20x - 10y + 25 = 0**

Explanation :

See Fig. Let m be the slope of the line PQ. Since ΔPQR = 45°, we have

Therefore, the combined equation of the lines PQ and PR is