(B) The length of the perpendicular $d$ from a point $(x_1, y_1)$ to the line $ax + by + c = 0$ is given by the formula: $d = \left| \frac{ax_1 + by_1

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(B) The length of the perpendicular $d$ from a point $(x_1, y_1)$ to the line $ax + by + c = 0$ is given by the formula: $d = \left| \frac{ax_1 + by_1 + c}{\sqrt{a^2 + b^2}} \right|$.Given point $(x_1, y_1) = (1, -2)$ and the line $12x + 5y + 63 = 0$.Substituting the values into the formula:$d = \left| \frac{12(1) + 5(-2) + 63}{\sqrt{12^2 + 5^2}} \right|$$d = \left| \frac{12 - 10 + 63}{\sqrt{144 + 25}} \right|$$d = \left| \frac{65}{\sqrt{169}} \right|$$d = \left| \frac{65}{13} \right| = 5 \text{ units.}$

Class 11 Mathematics Straight Lines Distance between two lines, Perpendicular distance of the line from a point, Position of point w.r.t. line

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The length of the perpendicular from $(1, -2)$ to the line $12x + 5y + 63 = 0$ is

AP EAMCET 2020 All AP EAMCET

A
$4$ units
B
$5$ units
C
$6$ units
D
$\frac{85}{13}$ units

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Straight Lines

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Distance between two lines, Perpendicular distance of the line from a point, Position of point w.r.t. line

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The length of the perpendicular from $(1, -2)$ to the line $12x + 5y + 63 = 0$ is

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If $p$ and $q$ are lengths of the perpendiculars from the origin to the lines $x \sec \theta + y \operatorname{cosec} \theta = k$ and $x \cos \theta - y \sin \theta = k \cos 2\theta$ respectively,then

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