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If the lines L1a n dL2 are tangents to 4...

If the lines `L_1a n dL_2` are tangents to `4x^2-4x-24 y+49=0` and are normals for `x^2+y^2=72 ,` then find the slopes of `L_1` and `L_2dot`

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To solve the problem, we need to find the slopes of the lines \( L_1 \) and \( L_2 \) that are tangents to the parabola given by the equation \( 4x^2 - 4x - 24y + 49 = 0 \) and also normals to the circle given by \( x^2 + y^2 = 72 \). ### Step 1: Rewrite the Parabola Equation First, we rewrite the equation of the parabola in a more standard form. The given equation is: \[ 4x^2 - 4x - 24y + 49 = 0 \] We can rearrange it as: ...
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