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If the foot of the perpendicular from the origin to a straight line is at `(3,-4)` , then find the equation of the line.

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The correct Answer is:
3x-4y=25
Let P(3,-4) be the foot of the perpendicular from the origin O on the required line. Then the slope of OP is
`(-4-0)/(3-0) = -(4)/(3)`
Therefore, the slope of the required line is 3/4.
Hence, its equation is
`y+4 = (3)/(4)(x-3)`
or 3x-4y = 25
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CENGAGE PUBLICATION-STRAIGHT LINES-CONCEPT APPLICATION EXERCISE 2.1
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  2. If the middle points of the sides B C ,C A , and A B of triangle A B C...

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  3. Find the equations of the lines which pass through the origin and are ...

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  4. If (-2,6) is the image of the point (4,2) with respect to line L=0, th...

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  5. Find the area bounded by the curves x+2|y|=1 and x=0 .

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  6. Find the equation of the straight line passing through the intersectio...

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  7. If the foot of the perpendicular from the origin to a straight line is...

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  8. A straight line through the point (2,2) intersects the lines sqrt(3)x+...

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  9. The equation of the straight line passing through the point (4. 3) and...

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  10. A straight line through the point A(3, 4) is such that its intercept ...

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  11. A straight line L is perpendicular to the line 5x-y=1 . The area of th...

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  12. One side of a rectangle lies along the line 4x+7y+5=0. Two of its vert...

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  13. A line L1=3y-2x-6=0 is rotated about its point of intersection with th...

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  14. The diagonals A C and B D of a rhombus intersect at (5,6)dot If A=(-3,...

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  15. Find the equation of the straight line which passes through the origin...

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  16. A line intersects the straight lines 5x-y-4=0 and 3x-4y-4=0 at A and B...

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  17. In the given figure, PQR is an equilateral triangle and OSPT is a squa...

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  18. Two fixed point A and B are taken on the cordinate axes such that OA =...

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  19. A regular polygon has two of its consecutive diagonals as the lines sq...

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  20. Find the direction in which a straight line must be drawn through th...

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