Which is the equation of the line perpendicular to $4 x - 5 y = 17$ that passes through the point $(5, 2)$ ?

4 x - 5 y = 10

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5 x + 4 y = 33

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4 x + 5 y = 30

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5 x - 4 y = 17

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y = \frac{- 5}{4} x + \frac{15}{2}

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Solution

The correct option is C $5 x + 4 y = 33$
The given line is $4 x - 5 y = 17$

Slope of the line is $\frac{4}{5}$

If two lines are perpendicular then their slopes are related with the relation $m_{1} . m_{2} = - 1$

If the other line is perpendicular to given line then slope of the line will be $\frac{- 1}{m}$

Slope of the line will be $- \frac{5}{4}$

Also the line passes thriugh the point $(5, 2)$ .

Writing the equation of a line with slope $- \frac{5}{4}$ and passing through point $(5, 2)$ , we get,

$\Rightarrow (y - 2) = - \frac{5}{4} (x - 5)$

$\Rightarrow 5 x + 4 y = 33$

Correct option is $B$

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Similar questions

4 x + 5 y = 10; 5 x + 4 y = 17

What is the equation of chord of contact of tangents drawn from P(10, 8) to the ellipse
$\frac{x^{2}}{25} + \frac{y^{2}}{16} = 1$ .

x + y = 30

A = (5, 0)

B = (0, 4)

P

| P A |^{2} - | P B |^{2} = 9

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