Question

Statement 1: If a line $L=0$ is tangent to the circle $S=0$, then it will also be a tangent to the circle $S+\lambda L=0$

Statement 2: If a line touches a circle, then perpendicular distance of the line from the centre of the circle is equal to the radius of the circle.

• A. Statement 1 is true, statement 2 is true, statement 2 is correct explanation for statement 1
• B. Statement 1 is true, Statement 2 is true, statement 2 is NOT a correct explanation for statement 1
• C. Statement 1 is true, Statement 2 is false
• D. Statement 1 is false, statement 2 is true

Answer 1

The correct option is A

Statement 1 is true, statement 2 is true, statement 2 is correct explanation for statement 1

Statement 1

0 is a tangent to a circle $S=0$

$S+\lambda L$ is the equation of family of circles which touches $L=0$

So, $L=0$ is also a tangent to family of circles $S+\lambda L$

Statement 1 is correct

Statement 2: If line touches a circle, it is tangent to the circle.

Perpendicular distance from the centre of the circle to the line (tangent) is radius of circle.

Statement 2 is also correct.

Statement (2) is also a correct explanation for statement (1)