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Thread: conics

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    conics

    so i have two tangents, and I have to find the point of intersection but i cant get anywhere when i do it

    tangents:
    y(3cosx)-x(2sinx)=6 and y(3sinx) +x(2cosx)=6

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    Re: conics

    Quote Originally Posted by nrumble42 View Post
    so i have two tangents, and I have to find the point of intersection but i cant get anywhere when i do it

    tangents:
    y(3cosx)-x(2sinx)=6 and y(3sinx) +x(2cosx)=6
    Are you sure those should be cos(x) and sin(x) instead of something like cos(theta) and sin(theta)? They wouldn't be straight lines as you've written them.
    pikachu975 likes this.

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    Re: conics

    Quote Originally Posted by InteGrand View Post
    Are you sure those should be cos(x) and sin(x) instead of something like cos(theta) and sin(theta)? They wouldn't be straight lines as you've written them.
    ahh yeah sorry, it does say theta

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    Re: conics

    bump

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    Re: conics

    Quote Originally Posted by nrumble42 View Post
    bump
    Now that those are cos(theta) etc., all you need to do is find the intersection of two lines. This can be done by solving for x in one of the lines (in terms of y), and plugging this into the other line's equation (i.e. standard procedure of solving two simultaneous linear equations in two unknowns).

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    Re: conics

    Quote Originally Posted by nrumble42 View Post
    so i have two tangents, and I have to find the point of intersection but i cant get anywhere when i do it

    tangents:
    y(3cosx)-x(2sinx)=6 and y(3sinx) +x(2cosx)=6
    Rearranging first tangent equation for x in terms of y:
    3ycosA - 2xsinA = 6
    2xsinA = 3ycosA - 6
    x = 3(ycosA - 2)/2sinA

    Sub this into second equation
    3ysinA + 2xcosA = 6
    3ysinA + 3cosA(ycosA-2)/sinA = 6
    3ysin^2 A + 3ycos^2 A - 6cosA = 6sinA
    3y (sin^2 A + cos^2 A) = 6(sinA + cosA)
    y = 2(sinA+cosA)

    Sub y into the first tangent equation
    6cosA(sinA+cosA) - 2xsinA = 6
    6sinAcosA + 6cos^2 A - 2xsinA = 6
    6sinAcosA + 6 - 6sin^2 A - 2xsinA = 6
    6sinAcosA - 6sin^2 A = 2xsinA
    3cosA - 3sinA = x (sinA doesn't = 0)
    x = 3(cosA-sinA)

    Therefore they intersect at x = 3(cosA-sinA), y = 2(sinA+cosA)
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