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Question

Find the equations to the common tangents of the circle x2+y2+4ax=0 and parabola y2=4ax.

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Solution

x2+4ax+y2=0x2+4ax+4a2+y2=4a2(x+2a)2+y2=4a2......(i)y2=4ax.........(ii)
By tracing the circle and the parabola we can clearly see that they touch each other along the y axis
So the equation of common tangent is x=0.

697182_641134_ans_d33f63125c3f4143b9d5ac92ce0fdd02.png

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