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Thread: tangent

  1. #1
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    tangent

    hi, could someone show me the steps to answering this question please?

    show that the lengths of the tangents from the point $\displaystyle (h, k)$ to the circle $\displaystyle x^2 + y^2 + 2fx + 2gy + c = 0$ are $\displaystyle \sqrt {h^2 + k^2 + 2fh + 2gk + c}$

    thanks, Mark
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  2. #2
    Senior Member pacman's Avatar
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    show that the lengths of the tangents from the point to the circle are

    -------------------------------------------------------------------------------------------------------------------------------------------------------

    equation of a circle: (x + f)^2 + (y + g)^2 = 2 - c = (sqrt(2 - c))^2.

    a line tangent to circle forms a right triangle, where the point of tangency as the right angle, one point at the center of a circle (-f,-g) and the other at a certain point (h,k.)

    use distance formula . . . .
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  3. #3
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    hi, i sort of see where you're going with that. but wouldn't there be a left over or something that you'd have to minus after you put the equation into brackets ie $\displaystyle f^2$ and $\displaystyle g^2$ in

    $\displaystyle (x + f)^2 - f^2 + (y + g)^2 - g^2 = - c$
    $\displaystyle \implies$$\displaystyle (x + f)^2 + (y + g)^2 = - c + g^2 + f^2$

    or is that wrong?
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