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Prove that the line through the point (x...

Prove that the line through the point `(x_1, y_1)`and parallel to the line `A x+B y+C=0`is `A(x-x_1)+B(y-y_1)=0`.

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Given line Ax+By+C=0,
Slope of the given line is `-A div B`
Required line is passing through (x1 , y1)
`( y -y1) = (-A div B) times (x-x1)`
...
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Prove that the line through the point x_1 , y_1) and parallel to the line Ax+By+C=0 is A(x-x_1) + B (y-y_1)=0 .

Show that the equation of a line passing through a given point (x_(1),y_(1)) and perpendicular to the line ax+by +c =0 is b(x- x_(1))-a(y-y_(1)) =0.

Knowledge Check

  • Joint equation of lines passing through the origin, and parallel to the lines y-m_(1)x+c_(1) and y=m_(1)x+c_(2) , is

    A
    `m_(1)m_(2)x^(2)-(m_(1)_m_(2))xy+y^(2)=0`
    B
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    C
    `m_(1)m_(2)y^(2)-(m_(1)+m_(2))xy+x^(2)=0`
    D
    `m_(1)m_(2)y^(2)+(m_(1)+m_(2))xy+x^(2)=0`

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