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Distance of origin from the line (1+sqrt...

Distance of origin from the line `(1+sqrt3)y+(1-sqrt3)x=10` along the line `y=sqrt3x+k`

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The distance of the point (1,-5,""9) from the plane x-y+z=5 measured along the line x=y=z is : (1) 3sqrt(10) (2) 10sqrt(3) (3) (10)/(sqrt(3)) (4) (20)/3

Distance of point (1,3) from the line 2x-3y+9=0 along x-y+1=0

Knowledge Check

  • The equations of lines passing through the point (1,0) and at distance of (sqrt(3))/(2) units from the origin are (i) sqrt(3)x+y-sqrt(3)=0,sqrt(3)x-ysqrt(3)=0 (ii) sqrt(3)x+y+sqrt(3)=0,sqrt(3)x-y+sqrt(3)=0 (iii) x+sqrt(3)y-sqrt(3)=0,x-sqrt(3)y-sqrt(3)=0 (iv) none of these

    A
    `sqrt(3)x+y-sqrt(3)=0,sqrt(3)x-ysqrt(3)=0`
    B
    `sqrt(3)x+y+sqrt(3)=0,sqrt(3)x-y+sqrt(3)=0`
    C
    `x+sqrt(3)y-sqrt(3)=0,x-sqrt(3)y-sqrt(3)=0`
    D
    none of these

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    Find the distance of the point (2,3) from the line 2x-3y+9=0 measured along a line x-y+1=0.

    Prove that the locus of the point of intersection of the lines sqrt3 x -y -4 sqrt3 k =0 and sqrt3 k x+ ky - 4 sqrt3 =0, for different values of k, is a hyperbola whose eccentricity is 2.

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    The distance of the point (1, 2, 3) from the plane x+y-z=5 measured along the straight line x=y=z is 5sqrt(3) (2) 10sqrt(3) (3) 3sqrt(10) 3sqrt(5) (5) 2sqrt(5)

    The equation of the lines passing through the point (1,0) and at a distance (sqrt(3))/2 from the origin is (a) sqrt(3)x+y-sqrt(3) =0 (b) x+sqrt(3)y-sqrt(3)=0 (c) sqrt(3)x-y-sqrt(3)=0 (d) x-sqrt(3)y-sqrt(3)=0

    The equation of the lines passing through the point (1,0) and at a distance (sqrt(3))/2 from the origin is (a). sqrt(3)+y-sqrt(3) =0 (b). x+sqrt(3)y-sqrt(3)=0 (c). sqrt(3)x-y-sqrt(3)=0 (d). x-sqrt(3)y-sqrt(3)=0

    The graph of straight line y = sqrt(3)x + 2sqrt(3) is :

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