Question

Assertion :The equation of circle having radius $\sqrt{10}$ and a diameter along line $2x+y=5$is $x^2+y^2-6x+2y=0$ Reason: $2x+y=5$ is a tangent to the circle $x^2+y^2-6x+2y=0.$

• A. Assertion is true, Reason is true, Reason is a correct explanation for Reason.
• B. Assertion is true ; Reason is false.Assertion is true, Reason is true, Reason is not a correct explanation for Reason.
• C. Assertion is false, Reason is true.
• D. Assertion is true ; Reason is false.

Answer 1

The correct option is D Assertion is true ; Reason is false.

Equation of circle given:

$\Rightarrow x^2+y^2-6x+2y=0$

$\therefore$ Centre $\to (3,-1)\to (-g,-f)$

$(3,-1)$ satisfies $2x+y=5$

$(\because 2(3)-1=5)$

$\therefore 2x+y=5$ represents diameter

Radius of circle $=\sqrt{g^2+f^2-c}$

$=\sqrt{9+1-0}$

$=\sqrt{10}$

Hence, assertion is true.

$\because 2x+y=5$ is diameter line , hence it cannot be the tangent to the given circle.

$\therefore$ Assertion is true, reason is false.

$\therefore D)$ Correct.