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Exercise 6.2 · Q22

Q.Find the differential equation of all parabolas having length of latus rectum 4a4a and axis parallel to the X-axis.

Maharashtra MsbshseTextbookSubjectiveImportance★★★★★
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A parabola with latus rectum 4a4a and axis parallel to the X-axis has equation (y−k)2=4a(x−h)(y-k)^2=4a(x-h), with h,kh,k arbitrary (aa fixed). Differentiate: 2(y−k)dydx=4a2(y-k)\dfrac{dy}{dx}=4a, so (y−k)=2ady/dx(y-k)=\dfrac{2a}{dy/dx}. Differentiate again: (dydx)2+(y−k)d2ydx2=0\left(\dfrac{dy}{dx}\right)^2+(y-k)\dfrac{d^2y}{dx^2}=0. Substituting (y−k)(y-k) and multiplying by …

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