InterviewSolution
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InterviewSolution
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The number of normal (s) to the parabola `y^2=8x` through (2, 1) is (B) 2 (A) 1 (D) 3 (C) 0 |
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Answer» Equation of the normal of the parabola ` y^2 = 4ax` is given by, ` y = mx - 2am-am^3->(1)` Now, in the given parabola, `y^2 = 8x` `a = 2` Putting value of `a` in (1), `=>y = mx-4m-2m^3` At point `(2,1)` this equation becomes, `=>1= 2m-4m-2m^3` `=>2m^3+2m-1 = 0->(2)` We know, in a cubic equation, there are `3` roots. One root is always real and remaining two roots can either be real or complex. To find the roots, we will differentiate equation (2). `=>6m^2+2 = 0` `=>m^2 = -1/3` It means two roots are complex as square of `m` is negative. So, only ne root is real, which means we can have only one normal with the given conditions. |
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