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Show that x + y + 1 = 0 touches the cir...

Show that `x + y + 1 = 0` touches the circle
`x^(2) + y^(2) -3x + 7y 14 = 0` and find its
point of contact.

Answer

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Show that the tangent at (-1, 2) of the circle x^(2) + y^(2) - 4x -8y + 7 = 0 touches the circle x^(2) + y^(2) + 4x + 6y = 0 and also find its point of contact.

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Knowledge Check

  • If the line x+y+1=0 touches the circle x^(2)+y^(2)-3x+7y+14=0 then the point of contact is

    A
    (1,0)
    B
    (2,-3)
    C
    (5,3)
    D
    (-1,0)

  • If the tangent to the circle x^(2) + y^(2) = 5 at (1, -2) also touches the circle x^(2) + y^(2)- 8x + 6y + 20 = 0 , then the point of contact is,

    A
    (-1, 0)
    B
    (1, 0)
    C
    (3,-1)
    D
    (5, 2).

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    Explore conceptually related problems

    Show that the line 5x + 12y - 4 = 0 touches the circle x^(2)+ y^(2) -6x + 4y + 12 = 0

    Show that the line x + 2y - 4 = 0 touches the ellipse 3x^(2) + 4y^(2) = 12 also find the point of contact.

    The point where the line 4x - 3y + 7 = 0 touches the circle x^(2) + y^(2) - 6x + 4y - 12= 0 is

    If 4x-3y+7 = 0 is a tangent ot the circle repesented by x^(2) + y^(2) -6x + 4y - 12 = 0 , then find its point of contact.

    Show that the line 7x + 6y = 13 is a tangent to the parabola y^(2) - 7x- 8y + 14 = 0 and find the point of contact

    If 4x -3y +7 =0 is a tangent to the circle represented by x ^(2) + y^(2) -6x + 4y -12=0 , then find its points of contact.

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