A) \[x+4y+1=0\]
B) \[9x+4y+4=0\]
C) \[x-4y+36=0\]
D) \[9x-4y+4=0\]
Correct Answer: C
Solution :
Given that\[{{y}^{2}}=9x\]. Here, \[a=\frac{9}{4}\]. Now, equation of tangent to the parabola \[{{y}^{2}}=9x\] is \[y=mx+\frac{9/4}{m}\] If this tangent goes through the point \[(4,\,10),\] then \[10=4m+\frac{9}{4m}\]\[\Rightarrow \,(4m-9)(4m-1)=0\]\[\Rightarrow \,m=\frac{9}{4},\frac{1}{4}\] \ Equation of tangents are, \[4y=x+36\] and \[y=-2x-k\] or \[x-4y+36=0\] and \[9x-4y+4=0\].
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