Question

$A$ssertion($A$): $x+2y-3=0$ is a tangent to the circle $x^2+y^2-4x-6y+8=0$.
Reason (R) :If the perpendicular distance of a line from the center of a circle is the radius of the circle, then it is the tangent.
Then the correct answer is

• A. Both A and R are true and R is the correct explanation of A.
• B. Both A and R are true and R is not the correct explanation of A.
• C. A is true but R is false.
• D. A is false but R is true.

Answer 1

The correct option is A Both A and R are true and R is the correct explanation of A.

Assertion : $x+2y-3=0$ is a tangent to circle $x^2+y^2-4x-6y+8=0$ then from (2, 3) distance of $x+2y-3=0$ is equal to radius.
$\therefore \sqrt{5}=\left|\frac{2+6-3}{\sqrt{5}}\right|=\left|\sqrt{5}\right|$
that means, $x+2y-3=0$ is a tangent of Given circle.
Reason (R): If lines is tangent to circle, then perpendicular djistance of line from the centre of circle is the radius of the circle.
then both A and R are True and R is the correct explanation of A.