A) \[\frac{a}{m}\]
B) am
C) \[a{{m}^{2}}\]
D) \[-a{{m}^{2}}\]
Correct Answer: A
Solution :
If we replace x by y and y by x, then the line is \[y=mx+k\]and parabola\[{{y}^{2}}=4ay\]. Hence \[k=\frac{a}{m}\] Aliter: If \[x=my+k\]touches\[{{x}^{2}}=4ay\], then the quadratic \[{{(my+k)}^{2}}=4ay\] will have two real and equal roots i.e., \[{{B}^{2}}-4AC=0\], which will give us \[k=\frac{a}{m}\].
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