Question

Assertion :Statement-1: The circle $x^2+y^2-8x-4y+16=0$ touches the x-axis at the point $(4,0)$. Reason: Statement-2: The circle $(x-x_1{)}^2+(y-r{)}^2=r^2$ touches the x-axis at the point $\left(x_{1}0\right)$

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Both Assertion and Reason are incorrect

Answer 1

The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

Statement $2$ is true as the centre of the circle $\left(x_{1}r\right)$ is at a distance $r$.
which is the radius of the circle,from the x-axis and hence the circle touches x-axis and the point of contact is $\left(x_{1}0\right)$.
Circle in statement-$l$ is $(x-4{)}^2+(y-2{)}^2=(2{)}^2$ using statement-$2$. statement-$1$ is true.