| Statement 1: All the lines of the given family pass through the point (3, -2). |
| Statement 2: All the lines of the given family pass through a fixed point. |
A) Statement-1 is false, Statement-2 is true.
B) Statement-1 is true, Statement-2 is true and Statement-2 is correct explanation for statement-1
C) Statement-1 is true, Statement-2 is true and Statement-2 is NOT correct explanation for statement-1
D) Statement-11s true, Statement-2 is false.
Correct Answer: A
Solution :
\[2{{\sin }^{2}}\theta x+{{\cos }^{2}}\theta y=2\cos 2\theta \] Statement-1: The line passes through the point (3,-2) If \[6{{\sin }^{2}}\theta -2{{\cos }^{2}}\theta =2\cos 2\theta \] i.e. \[6(1-{{\cos }^{2}}\theta )-2{{\cos }^{2}}\theta =4{{\cos }^{2}}\theta -2\] Family of lines passes through the point of intersection of line 2 x - y + 4 = 0 and x = - 1 \[\therefore \]The point is (-1,2) \[\therefore \]Statement-2 is true.
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