Question

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​

Answer 1

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.

Answer 2

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

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