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$The orthogonal trajectories of the family of ellipses x^{2} + 2 y^{2} - y = c are family of parabola$ $y = c x^{2} + k, where k =$

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Correct option is D

x2+2y2−y=c2x+4yy1−y1=0⇒2x=−(4y−1)y1 Replace y1 by -1_dydx⇒2xdydx=4y−1⇒∫4dy4y−1=∫2dxx⇒4y−1=c1x2y=cx2+14 k=14

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The orthogonal trajectories of the family of ellipses x2+2y2−y=c are family of parabola y=cx2+k, where k=

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$The orthogonal trajectories of the family of ellipses x^{2} + 2 y^{2} - y = c are family of parabola$ $y = c x^{2} + k, where k =$