| Statement-1: Slope of tangents drawn from \[(4,\,\,10)\]) to parabola\[{{y}^{2}}=9x\]are\[\frac{1}{4},\,\,\frac{9}{4}\] |
| Statement-2: Every parabola is symmetric about its directrix |
A) Statement-1 is false, Statement-2 is true.
B) Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
C) Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
D) Statement-1 is true, Statement-2 is false.
Correct Answer: D
Solution :
\[y=mx+\frac{a}{m}\] \[10=4m-1\frac{9/4}{m}\Rightarrow 16{{m}^{2}}-40m+9=0\] \[{{m}_{1}}+{{m}_{2}}=\frac{40}{16}=\frac{5}{2};\,\,{{m}_{1}}{{m}_{2}}=\frac{9}{16}\] \[\Rightarrow \] \[{{m}_{1}}=\frac{1}{4},\,\,{{m}_{2}}=\frac{9}{4}\] every parabola is symmetric about its axis only Statement 1 is true.
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