Question

The perpendicular distance from the point (5, 4) on the line
2x + y + 6 = 0 is​

Answer 1

$2x + y + 6 = 0 \\ x = 5 \: and \: y = 4 \\ 2x + y + 6 = 0 \\ 2 \times 5 + 4 + 6 = 0 \\ 10 + 10 = 0 \\ 20 ≠ 0$

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Answer 2

EXPLANATION.

Perpendicular distance from point (5,4).

On the line : 2x + y + 6 = 0.

As we know that,

Length of perpendicular :

⇒ P = | ax₁ + by₁ + c/√a² + b² |.

⇒ P = | 2x + y + 6/√(2)² + (1)² |.

put the value of x and y in equation, we get.

⇒ p = | 2(5) + 4 + 6/√4 + 1 |.

⇒ p = | 10 + 4 + 6/√5 |.

⇒ p = | 20/√5 |.

⇒ p = | 2√5/√5 |.

⇒ p = | 2 |.

⇒ p = 2.

                                                                                                                         

MORE INFORMATION.

General equation of second degree.

ax² + 2hxy + by² + 2gx + 2fy + c = 0.

(a) = Represent a pair of two straight lines if,

$\sf \implies \Delta = \left[\begin{array}{ccc}a&h&g\\h&b&f\\g&f&c\end{array}\right] = 0$

(b) = Represent a circle if Δ ≠ 0, a = b, h = 0.

(c) = Represent conic section if,

⇒ Δ ≠ 0, a ≠ b,

⇒ h² > ab = Hyperbola.

⇒ h² = ab = Parabola.

⇒ h² < ab = Ellipse.