A) They both touch each other at P
B) They cut at right angles at P
C) The tangents to each curve at P make complementary angles with the x-axis
D) None of these
Correct Answer: C
Solution :
Solving \[{{x}^{2}}=4y\]and \[{{y}^{2}}=4x,\]we get \[x=0,\,\,y=0\] and \[x=4,\,y=4\]. Therefore the co-ordinates of P are (4,4). The equations of the tangents to the two parabolas at (4,4) are \[2x-y-4=0\] .....(i) \[x-2y+4=0\] .....(ii) Now, \[{{m}_{1}}=\]Slope of (i) \[=2,\]\[{{m}_{2}}=\]Slope of (ii) \[=\frac{1}{2}\] \\[{{m}_{1}}{{m}_{2}}=1\,\,\,i.e.,\,\,\,\tan {{\theta }_{1}}\tan {{\theta }_{2}}=1\].
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