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If the line lx + my = 1 be a tangent to ...

If the line `lx + my = 1` be a tangent to the circle `x^(2)+y^(2)=a^(2)`, then the point `(l, m)` lies on

A

ellipse

B

parabola

C

circle

D

none

Text Solution

Verified by Experts

The correct Answer is:
C
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If the line lx+my+n=0 is tangent to the circle x^(2)+y^(2)=a^(2) , then find the condition.

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Knowledge Check

  • The line lx+my+n=0 is a tangent to the curve y=x-x^2+x^3 , then

    A
    `lgt0,mgt0`
    B
    `llt0,mlt0`
    C
    `lmgt0`
    D
    `lmlt0`

  • If lx + my + n = 0 is tangent to the parabola x^(2)=y , them

    A
    `t^(2)=2mn`
    B
    `i=4m^(2)n^(2)`
    C
    `m^(2)=4/n`
    D
    `l^(2)=4mn`

  • If a line, y = mx + c is a tangent to the circle, (x-1)^2 + y^2 =1 and it is perpendicular to a line L_1 , where L_1 is the tangent to the circle x^2 + y^2 = 8 at the point (2, 2), then :

    A
    `C^2 + 2c -1=0`
    B
    `c^2 -2 c +1=0`
    C
    `c^2 -2c -1=0`
    D
    `c^2 + 2c+2=0`

    • Similar Questions

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    The equation of the line parallel to the tangent to the circle x^(2)+y^(2)=r^(2) at the point (x_(1),y_(1)) and passing through origin is

    If the line lx+my-1=0 touches the circle x^(2)+y^(2)=a^(2), then prove that (l,m) lies on a circle.

    If lx+my=1 touches the circle x^(2)+y^(2)=a^(2) , prove that the point (l,m) lies on the circle x^(2)+y^(2)=a^(-2)

    If the line lx+my+n=0 touches the circle x^(2)+y^(2)=a^(2), then prove that (l^(2)+m^(2))^(2)=n^(2)

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