Question

The equations of the lines through the point (3, 2) which make an angle of 45o with the line x - 2y = 3 are

• A. (A) 3x - y = 7 and x + 3y = 9
• B. (B) x - 3y = 7 and 3x + y = 9
• C. (C) x - y = 3 and x + y = 2
• D. (D) 2x + y = 7 and x - 2y = 9

Answer 1

Answer: (A)

(A) 3x - y = 7 and x + 3y = 9

Answer 2

Explanation:
The slope of line x−2y=3 is 12Let the slope of required lines is m∴tan⁡45∘=±|22−m|⇒1+m2=±(12−m)m2∣⇒−12=3m2⇒m=−13or 1+m2=−12+m⇒m2=32⇒m=3∴ Equation of line with slope m=1−3 and passing through (3,2), is(y−2)=1−3(x−3)⇒y−6=−x+3⇒x+3y=9And another equation of line with slopem=3 and passing through (3,2), is(y−2)=3(x−3)⇒y−2=3x−9⇒3x−y=7