| Direction: Assertion- Reaction type. Each of these contains tow statements: Statement I (Assertion), Statement II (Reason). Each of these questions also has four alternative choices, only one of which is correct. You have to select the correct choices from the codes [a], [b], [c] and [d] given below: |
| Statement I: If normal at the ends of double ordinate x = 4 of parabola y2 = 4x meet the curve again at P and P' respectively, then PP' = 12unit. |
| Statement II: If normal at \[{{\text{t}}_{\text{1}}}\] of y2 = 4ox meet the parabola again at \[{{\text{t}}_{2}},\] then \[{{\text{t}}_{2}}=-{{t}_{1}}\frac{2}{{{t}_{1}}}.\] |
A) Statement I is true; Statement II is true; Statement II is not a correct explanation for Statement I
B) Statement I is true; Statement II is false.
C) Statement I is false; Statement II is true.
D) Statement I is true; Statement II is true; Statements is the correct explanation for Statement I.
Correct Answer: B
Solution :
End points of double ordinate x = 4 of parabola y2 = 4 x are \[(4\pm 4).\] \[\Rightarrow \] \[{{t}_{1}}=\pm 2\] \[\because \] \[{{t}_{2}}=-{{t}_{1}}-\frac{2}{{{t}_{1}}}\] \[=\pm 3\] \[\Rightarrow \]Points P (9,6) and P' (9,-6). \[\therefore \]\[pp'\sqrt{{{(9-9)}^{2}}+{{(-6-6)}^{2}}}=12\]unit.
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