The equation of straight line through (1,3) and perpendicular to 2x +y+3=0 is
A) 2x-Y+1-O B) x+y-4-O
C) 2x-3Y+7=O D) x-2Y+5=O
Answers
EXPLANATION.
Equation of straight line through (1,3).
Perpendicular to the : 2x + y + 3 = 0.
As we know that,
Slope of the perpendicular line = b/a.
Slope of the line = m = 2x + y + 3 = 0.
⇒ Slope = m = 1/2.
As we know that,
Equation of the tangent.
⇒ (y - y₁) = m(x - x₁).
Put the values in the equation, we get.
⇒ (y - 3) = 1/2(x - 1).
⇒ 2(y - 3) = (x - 1).
⇒ 2y - 6 = x - 1.
⇒ x - 1 - 2y + 6 = 0.
⇒ x - 2y + 5 = 0.
Hence, option [D] is correct answer.
MORE INFORMATION.
Equation of straight line parallel to axes.
(1) = Equation of x-axes ⇒ y = 0.
(2) = Equation of a line parallel to x-axes at a distance of b ⇒ y = b.
(3) = Equation of y-axes ⇒ x = 0.
(4) = Equation of a line parallel to y-axes and at a distance of a ⇒ x = a.
Given :-
2x + y + 3 = 0
To Find :-
Equation
Solution :-
(y₂ - y₁) = m(x₂ - x₁)
y₂ = y
y₁ = 3
m = 1/2 (Slope)
x₂ = x
x₁ = 1
(y - 3) = 1/2(x - 1)
2 × (y - 3) = x - 1
(2 × y) - (2 × 3) = x - 1
2y - 6 = x - 1
2y - 6 - x + 1
(x - 2y) - (-6 + 1) = 0
(x - 2y) - (-5) = 0
x - 2y + 5 = 0
[tex][/tex]